S&DS 363 Homework 6
Evan Collins, Kelly Farley, Ken Stier
23 April 2021
# clear env
rm(list=ls())
# Load packages
library(car)
library(tidyverse)
library(MASS)
library(DiscriMiner)
library(klaR)
#library(aplpack)
library(fpc)
library(cluster)
library(ape)
library(amap)
# Packages pertinent to Ordination
library(vegan) # eggplant
#library(vegan3d)
library(mgcv)
#library(rgl)
library(dplyr)
library(magrittr)Contributors
Evan Collins (evan.collins@yale.edu)
Kelly Farley (kelly.farley@yale.edu)
Ken Stier (ken.stier@yale.edu)
The Dataset
Raw dataset: COVID-19 infection and death statistics from U.S. counties (sourced from NYT), combined with economic, education, and population data (sourced from various government agencies) and also survey responses about mask-wearing frequencies (sourced from NYT). 3141 complete observations on 19 metric variables and 6 categorical variables. To avoid any outliers due to population size differences between counties, all variables are scaled as a percentage of population. Variable descriptions can be found here.
Data of relevance for this pset:
This pset only explores the 67 counties in the best state, Florida.
We look at five continuous variables describing each county: Always_Wear_Mask_Survey, Median_Household_Income_Percent_of_State_Total_2019, Percent_Poverty_2019, Percent_Adults_Less_Than_HS, and Covid_Confirmed_Cases_as_pct. Note that Always_Wear_Mask_Survey and Covid_Confirmed_Cases_as_pct were multiplied by 100 to convert the value from a fraction to percent value (like the other variables). This data is stored in data_ord_base.
For additional continuous variables, we make an environmental dataset. We look at five additional continuous variables describing each county: Unemployment_Rate_2019, Death_Rate_2019, Birth_Rate_2019, Civilian_Labor_Force_2019_as_pct, Percent_Adults_Bachelors_or_Higher. Note that Civilian_Labor_Force_2019_as_pct was multiplied by 100 to convert the value from a fraction to percent value (like the other variables). This data is stored in data_ord_env.
# Process raw dataset as we have done in preceding psets
raw <- read.csv("https://evancollins.com/covid_and_demographics.csv")
# create categorical variables: rural-urban code (3 levels), region (4 variables)
# log transformations of our continuous variables
raw$logMedian_Household_Income_2019 <- log(raw$Median_Household_Income_2019 + 0.0001)
raw$logPercent_Poverty_2019 <- log(raw$Percent_Poverty_2019 + 0.0001)
raw$logCovid_Confirmed_Cases_as_pct <- log(raw$Covid_Confirmed_Cases_as_pct + 0.0001)# Base dataset of interest for this pset - data_ord_base
data_ord <- raw[raw$State_Name=="Florida", ]
data_ord <- data_ord[, c(2, 9, 12, 13, 14, 22)]
data_ord_base <- data_ord
data_ord_base$Covid_Confirmed_Cases_as_pct <- 100*data_ord_base$Covid_Confirmed_Cases_as_pct
data_ord_base$Always_Wear_Mask_Survey <- 100*data_ord_base$Always_Wear_Mask_Survey
data_ord_base1 <- data_ord_base
data_ord_base <- data_ord_base1[,-1]
rownames(data_ord_base) <- data_ord_base1[,1] # rownames are county names
dim(data_ord_base)## [1] 67 5head(data_ord_base)## Always_Wear_Mask_Survey
## Alachua 75.1
## Baker 44.2
## Bay 54.8
## Bradford 38.1
## Brevard 60.7
## Broward 79.1
## Median_Household_Income_Percent_of_State_Total_2019
## Alachua 84.3
## Baker 102.1
## Bay 98.6
## Bradford 80.3
## Brevard 97.3
## Broward 103.8
## Percent_Poverty_2019 Percent_Adults_Less_Than_HS
## Alachua 18.4 7.6
## Baker 14.9 15.5
## Bay 12.1 9.7
## Bradford 21.0 21.7
## Brevard 9.4 8.0
## Broward 12.3 11.2
## Covid_Confirmed_Cases_as_pct
## Alachua 7.984597
## Baker 10.838754
## Bay 10.043788
## Bradford 9.712422
## Brevard 5.189537
## Broward 9.243293plot(data_ord_base)
# Enviromental variables dataset - data_ord_env
data_ord_env_county <- raw[raw$State_Name=="Florida", ]
data_ord_env_county <- data_ord_env_county[, c(2, 10, 18, 19, 25, 15)]
data_ord_env <- data_ord_env_county
data_ord_env$Civilian_Labor_Force_2019_as_pct <- 100*data_ord_env$Civilian_Labor_Force_2019_as_pct
data_ord_env1 <- data_ord_env
data_ord_env <- data_ord_env1[,-1]
rownames(data_ord_env) <- data_ord_env1[,1] # rownames are county names
dim(data_ord_env)## [1] 67 5head(data_ord_env)## Unemployment_Rate_2019 Death_Rate_2019 Birth_Rate_2019
## Alachua 2.9 7.7 10.3
## Baker 3.1 9.5 11.2
## Bay 3.9 11.0 12.3
## Bradford 3.1 12.5 10.2
## Brevard 3.2 12.5 8.8
## Broward 3.0 8.2 11.2
## Civilian_Labor_Force_2019_as_pct Percent_Adults_Bachelors_or_Higher
## Alachua 51.74526 42.5
## Baker 40.57515 13.4
## Bay 48.21556 22.8
## Bradford 39.22556 10.6
## Brevard 47.19508 29.3
## Broward 53.28404 31.91
Fit Correspondence Analysis to your data.
All columns of data_ord_base contains the variable data. Correspondence analysis is performed using the cca() function.
# No negative data anyways
# data_ord_base <- data_ord_base[apply(data_ord_base, 1, sum) > 0, ]
#Perform correspondence analysis
data_ord_base_ca <- cca(data_ord_base)
# inertia is measure of departure from ind model; if no relationships from rows and columns; in this case, household income, percent poverty are related; other variables are not so strongly related; if inertia smaller - less structure to data in 5-D 2
Discuss the inertia, make a two dimensional plot of the first two CA directions.
summary(data_ord_base_ca)##
## Call:
## cca(X = data_ord_base)
##
## Partitioning of scaled Chi-square:
## Inertia Proportion
## Total 0.05033 1
## Unconstrained 0.05033 1
##
## Eigenvalues, and their contribution to the scaled Chi-square
##
## Importance of components:
## CA1 CA2 CA3 CA4
## Eigenvalue 0.03606 0.009955 0.002521 0.001793
## Proportion Explained 0.71649 0.197808 0.050087 0.035616
## Cumulative Proportion 0.71649 0.914297 0.964384 1.000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
##
##
## Species scores
##
## CA1 CA2 CA3
## Always_Wear_Mask_Survey -0.04389 -0.14340 0.002602
## Median_Household_Income_Percent_of_State_Total_2019 -0.12367 0.07293 -0.005506
## Percent_Poverty_2019 0.36607 0.01375 0.119450
## Percent_Adults_Less_Than_HS 0.43620 0.01442 -0.127072
## Covid_Confirmed_Cases_as_pct 0.23445 0.14590 0.048594
## CA4
## Always_Wear_Mask_Survey 0.01398
## Median_Household_Income_Percent_of_State_Total_2019 -0.01211
## Percent_Poverty_2019 -0.06152
## Percent_Adults_Less_Than_HS -0.01670
## Covid_Confirmed_Cases_as_pct 0.17146
##
##
## Site scores (weighted averages of species scores)
##
## CA1 CA2 CA3 CA4
## Alachua -0.2579870 -1.60706 2.77217 0.400127
## Baker 0.0280475 1.66967 -0.23324 0.190358
## Bay -0.5365473 0.59860 0.64355 1.166522
## Bradford 1.2707134 1.41794 -0.27880 -1.401618
## Brevard -1.0058699 -0.33752 -0.04251 -0.470399
## Broward -0.6113475 -0.97532 0.23822 1.265977
## Calhoun 1.3900689 0.02428 -0.16307 0.484268
## Charlotte -0.6966676 -0.74566 0.09810 -0.536160
## Citrus -0.1394691 -0.75200 0.65413 -0.816689
## Clay -1.2865849 1.56298 -0.68961 -0.642613
## Collier -0.9516428 0.62048 -1.37787 -0.424347
## Columbia 0.4255024 1.39936 0.85239 0.584438
## DeSoto 1.4124015 -1.54893 -1.23015 -0.215095
## Dixie 1.5911653 0.66090 0.41171 -1.853031
## Duval -0.4777867 -0.10803 0.67291 0.565342
## Escambia -0.1999783 0.46290 1.84232 0.884221
## Flagler -1.1162511 0.02829 -0.11021 -1.040040
## Franklin 1.0293941 1.18179 -0.08849 -0.391357
## Gadsden 1.1331068 -0.38765 0.06956 1.041970
## Gilchrist 0.2923450 0.49907 0.04248 -1.120320
## Glades 0.9602104 -1.33106 -1.49877 -1.420773
## Gulf 0.2524635 1.27854 0.02130 2.094265
## Hamilton 2.4514005 1.14909 2.54929 -2.856752
## Hardee 1.6243491 0.18401 -0.48894 -0.778705
## Hendry 1.6425587 -0.76661 -3.48737 -0.265267
## Hernando -0.2998987 -0.60987 -0.40381 -0.858329
## Highlands 0.2519377 -1.18798 -0.01501 -0.567841
## Hillsborough -0.5718720 -0.69371 0.19420 -0.141031
## Holmes 1.4478480 -0.62345 -0.36468 0.727175
## Indian River -0.6894247 0.04277 -0.33385 -0.587752
## Jackson 1.2323901 -0.11028 0.52615 1.685731
## Jefferson 0.5199624 -1.08804 0.05242 0.654107
## Lafayette 1.5911661 1.87293 -0.72446 3.927492
## Lake -0.6913000 -0.39668 -0.26513 -0.220985
## Lee -0.6743885 -0.12695 -0.50324 -0.126535
## Leon -0.2733104 -0.75881 3.57284 0.209794
## Levy 0.6182007 -1.17123 0.61102 -0.978715
## Liberty 1.2580903 0.50200 1.53857 0.360751
## Madison 1.7895438 1.25426 1.29302 -1.010829
## Manatee -0.7719348 0.15722 -0.19547 -0.142531
## Marion 0.0007508 -0.19202 0.44339 -0.551968
## Martin -1.1684693 -0.20071 -0.58139 -0.246356
## Miami-Dade 0.2996775 -0.69843 -0.18127 2.816490
## Monroe -1.0677179 -0.94099 0.03983 0.703280
## Nassau -1.1748135 1.88767 -0.34885 -0.333700
## Okaloosa -0.9045129 1.42972 0.35211 -0.007087
## Okeechobee 0.9644400 -1.46129 -1.64082 -0.286844
## Orange -0.6481869 -0.54586 0.03647 0.195285
## Osceola -0.1761811 -1.10587 0.15055 1.364315
## Palm Beach -0.7863143 -0.73505 -0.34040 0.290999
## Pasco -0.6495546 -1.12949 -0.22874 -0.211219
## Pinellas -0.7857529 -1.30050 0.41633 0.359708
## Polk -0.0173068 -0.63077 -0.47020 -0.120923
## Putnam 1.0882213 -0.83097 0.84041 -1.396901
## St. Johns -1.8246946 1.91832 -0.46595 -0.771806
## St. Lucie -0.4973983 -0.51158 -1.18380 -0.222083
## Santa Rosa -0.9793112 1.73872 0.06881 0.120004
## Sarasota -1.3034658 -0.42690 -0.25311 0.107948
## Seminole -1.4009072 -0.32091 0.34367 -0.478166
## Sumter -1.1177304 -0.06506 -0.32542 -0.421412
## Suwannee 0.8290661 1.75865 -0.30903 0.183506
## Taylor 1.4076618 0.46177 -0.43854 0.710780
## Union 1.0743577 0.92255 -0.77718 -0.237763
## Volusia -0.5157772 -0.59935 0.52913 -0.612641
## Wakulla -0.3710730 1.56935 -0.22170 0.039781
## Walton -0.6230454 1.06728 -0.38047 0.383858
## Washington 1.0322373 -0.42952 0.54986 0.195862Inertia (equal to squared eigenvalues) is like variance and measures departures from the independence model. We see that the inertia value is 0.05033. The magnitude of inertia does not reflect more or less variance per se; it is reflective of the magnitude of the data. (Note that multiplying fractions by 100 to make values as percents did not increase this inertia magnitude).
In the “Proportion Explained” row, we can see that first CA direction explains 0.71649 (~72%) of the relation. The “Cumulative Proportion” by the second CA direction is 0.914297; hence, the first and second CA directions explain the vast majority of total inertia. The third and fourth CA directions have significantly smaller “Proportion Explained” values. This suggests that there are likely two major underlying discriminatory dimensions captured by the data.
#plot results
plot(data_ord_base_ca, main = "Correspondence Analysis for FL Counties", type = "n")
text(data_ord_base_ca, dis = "wa", labels = rownames(data_ord_base))
points(data_ord_base_ca, pch = 21, col = "red", bg = "yellow", cex = 1.2)
text(data_ord_base_ca, "species", col = "blue", cex = 0.8)
Add environmental variables.
plot(data_ord_base_ca, main = "Correspondence Analysis for FL Counties", type = "n")
points(data_ord_base_ca, pch = 19, col = "black", cex = 1)
text(data_ord_base_ca, "species", col = "blue", cex = 1.1)
#add environmental variables
fit <- envfit(data_ord_base_ca, data_ord_env, permutations = 1000)
plot(fit, col = "red", lwd = 3)
#get significance - all environmental variables are significant
fit##
## ***VECTORS
##
## CA1 CA2 r2 Pr(>r)
## Unemployment_Rate_2019 0.93609 -0.35176 0.2400 0.000999 ***
## Death_Rate_2019 0.61828 -0.78596 0.0084 0.784216
## Birth_Rate_2019 0.99605 0.08877 0.0450 0.228771
## Civilian_Labor_Force_2019_as_pct -0.97424 -0.22551 0.4110 0.000999 ***
## Percent_Adults_Bachelors_or_Higher -0.99468 -0.10305 0.6962 0.000999 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 1000We can see that all environmental variables are significant (p < 0.05) except Birth_Rate_2019 and Death_Rate_2019. We will omit these variables from the environmental variable dataset for future analyses.
data_ord_env <- subset(data_ord_env, select=-2)
data_ord_env <- subset(data_ord_env, select=-2)This plot is somewhat hard to read, so we try detrended correspondence analysis. This is even harder to read. DCA uses the decorana() function.
#detrended correspondence analysis
data_ord_base_dca <- decorana(data_ord_base)
plot(data_ord_base_dca, main = "DCA for Rural-Urban Type", type = "n")
text(data_ord_base_dca, display = c("sites"), labels = rownames(data_ord_base), cex = 0.86)
points(data_ord_base_dca, pch = 21, col = "red", bg = "yellow", cex = 0.6)
text(data_ord_base_dca, "species", col = "blue", cex = 0.6)
#add environmental variables
fit <- envfit(data_ord_base_dca, data_ord_env, permutations = 1000)
plot(fit, col = "red", lwd = 3)
3
Comment on whether or not there is any evidence of ‘data snaking’ in higher dimensional space.
pc1 <- princomp(data_ord_env, cor=TRUE)
source("http://reuningscherer.net/multivariate/r/ciscoreplot.R.txt")
ciscoreplot(pc1,c(1,2),data_ord_env[,1])## Warning in sqrt((5.99 - (y1vec^2)/x$sdev[comps[1]]^2) * x$sdev[comps[2]]^2):
## NaNs produced
## Warning in sqrt((5.99 - (y1vec^2)/x$sdev[comps[1]]^2) * x$sdev[comps[2]]^2):
## NaNs produced
There is no evidence of data snaking in higher dimensional space. Evidence of snaking would be a PCA score plot that looks like a horseshoe. However, the above scoreplot appears random and therefore does not indicate data snaking.
4
In a few sentences, describe what you conclude from your plot.
From our first plot in (2) of the first two CA directions, we should be able to find which counties are similar and what are the columns on which they are similar. Overall, the counties seem evenly and randomly scattered between the 4 quadrants- we do not note rows near columns, so there is not association not accounted for by the independence model. Generally, the first correspondence axis is associated with low income and low education and high COVID-19 rates, while the second correspondence axis is associated primarily with poor masking behaviors and high COVID-19 rates, perhaps indicating two different types of counties that are associated with high COVID-19 rates (those in poorer, disadvantaged areas and also those with poor masking behaviors). As one may expect, the percent poverty and percent of adults with less than a high school degree point in the same direction, while the median household income points in the opposite direction.
5
Perform Multidimensional Scaling (metric or non-metric) for 1, 2, and 3 dimensions.
results <- matrix(NA, 21, 5)
#j is number of dimensions to try
for (j in 1:5){
for (i in 1:20){
temp <- data_ord_base[shuffle(nrow(data_ord_base)), 1]
for (k in 2:12) { temp <- cbind(temp, data_ord_base[shuffle(nrow(data_ord_base)), k]) }
#store stress
results[i, j] <- metaMDS(temp, k = j, distance = "euclidean")$stress
}
results[21, j] <- metaMDS(data_ord_base, k = j, distance = "euclidean")$stress
}## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3943127
## Run 1 stress 0.568615
## Run 2 stress 0.4155144
## Run 3 stress 0.5683427
## Run 4 stress 0.4823638
## Run 5 stress 0.4505892
## Run 6 stress 0.5634953
## Run 7 stress 0.4540016
## Run 8 stress 0.4275637
## Run 9 stress 0.5211749
## Run 10 stress 0.4309893
## Run 11 stress 0.5681489
## Run 12 stress 0.5683828
## Run 13 stress 0.4647005
## Run 14 stress 0.4984322
## Run 15 stress 0.3902451
## ... New best solution
## ... Procrustes: rmse 0.021273 max resid 0.138805
## Run 16 stress 0.5267726
## Run 17 stress 0.5676467
## Run 18 stress 0.5642802
## Run 19 stress 0.5684096
## Run 20 stress 0.5387107
## *** No convergence -- monoMDS stopping criteria:
## 9: stress ratio > sratmax
## 11: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3822443
## Run 1 stress 0.5685735
## Run 2 stress 0.5686648
## Run 3 stress 0.4390485
## Run 4 stress 0.5673861
## Run 5 stress 0.5573369
## Run 6 stress 0.5682804
## Run 7 stress 0.4462717
## Run 8 stress 0.5682225
## Run 9 stress 0.5685445
## Run 10 stress 0.5676567
## Run 11 stress 0.5251719
## Run 12 stress 0.560842
## Run 13 stress 0.4679827
## Run 14 stress 0.5349863
## Run 15 stress 0.437663
## Run 16 stress 0.4702736
## Run 17 stress 0.5614889
## Run 18 stress 0.438425
## Run 19 stress 0.5685492
## Run 20 stress 0.5671231
## *** No convergence -- monoMDS stopping criteria:
## 4: stress ratio > sratmax
## 16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3757599
## Run 1 stress 0.5339853
## Run 2 stress 0.5646727
## Run 3 stress 0.5411931
## Run 4 stress 0.5686678
## Run 5 stress 0.5673905
## Run 6 stress 0.4747698
## Run 7 stress 0.5399998
## Run 8 stress 0.4013165
## Run 9 stress 0.5670451
## Run 10 stress 0.4061334
## Run 11 stress 0.5681209
## Run 12 stress 0.5679906
## Run 13 stress 0.5214608
## Run 14 stress 0.5681227
## Run 15 stress 0.3790507
## Run 16 stress 0.3752992
## ... New best solution
## ... Procrustes: rmse 0.012356 max resid 0.04729131
## Run 17 stress 0.5683744
## Run 18 stress 0.5684017
## Run 19 stress 0.379117
## Run 20 stress 0.5681329
## *** No convergence -- monoMDS stopping criteria:
## 4: stress ratio > sratmax
## 16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.375132
## Run 1 stress 0.4857807
## Run 2 stress 0.5677602
## Run 3 stress 0.4879986
## Run 4 stress 0.4449863
## Run 5 stress 0.5680326
## Run 6 stress 0.5685972
## Run 7 stress 0.5673691
## Run 8 stress 0.5686677
## Run 9 stress 0.5681667
## Run 10 stress 0.4889232
## Run 11 stress 0.4566322
## Run 12 stress 0.3758467
## Run 13 stress 0.5681471
## Run 14 stress 0.5607571
## Run 15 stress 0.4460828
## Run 16 stress 0.5670206
## Run 17 stress 0.4473818
## Run 18 stress 0.4237776
## Run 19 stress 0.4626733
## Run 20 stress 0.5683772
## *** No convergence -- monoMDS stopping criteria:
## 6: stress ratio > sratmax
## 14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3667049
## Run 1 stress 0.5671196
## Run 2 stress 0.4074365
## Run 3 stress 0.5681924
## Run 4 stress 0.5681904
## Run 5 stress 0.3664824
## ... New best solution
## ... Procrustes: rmse 0.006984227 max resid 0.03158248
## Run 6 stress 0.568438
## Run 7 stress 0.5673793
## Run 8 stress 0.4409874
## Run 9 stress 0.5415778
## Run 10 stress 0.4075634
## Run 11 stress 0.3661472
## ... New best solution
## ... Procrustes: rmse 0.007118024 max resid 0.0246053
## Run 12 stress 0.4158464
## Run 13 stress 0.4256755
## Run 14 stress 0.5681009
## Run 15 stress 0.5668567
## Run 16 stress 0.567953
## Run 17 stress 0.3584335
## ... New best solution
## ... Procrustes: rmse 0.08064193 max resid 0.5662588
## Run 18 stress 0.4831527
## Run 19 stress 0.4380623
## Run 20 stress 0.5453604
## *** No convergence -- monoMDS stopping criteria:
## 1: stress ratio > sratmax
## 19: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3745206
## Run 1 stress 0.5654734
## Run 2 stress 0.5683428
## Run 3 stress 0.527673
## Run 4 stress 0.4319327
## Run 5 stress 0.552586
## Run 6 stress 0.5677485
## Run 7 stress 0.4005326
## Run 8 stress 0.565497
## Run 9 stress 0.5451122
## Run 10 stress 0.5670775
## Run 11 stress 0.5685265
## Run 12 stress 0.4076209
## Run 13 stress 0.4304182
## Run 14 stress 0.5094548
## Run 15 stress 0.4104833
## Run 16 stress 0.5620525
## Run 17 stress 0.4477147
## Run 18 stress 0.4541433
## Run 19 stress 0.5629403
## Run 20 stress 0.4394825
## *** No convergence -- monoMDS stopping criteria:
## 9: stress ratio > sratmax
## 11: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3826193
## Run 1 stress 0.3841599
## Run 2 stress 0.3839553
## Run 3 stress 0.4314456
## Run 4 stress 0.4659825
## Run 5 stress 0.5682937
## Run 6 stress 0.5237444
## Run 7 stress 0.4524955
## Run 8 stress 0.5657742
## Run 9 stress 0.5682134
## Run 10 stress 0.5684591
## Run 11 stress 0.5675152
## Run 12 stress 0.5003737
## Run 13 stress 0.5042352
## Run 14 stress 0.4177035
## Run 15 stress 0.4826258
## Run 16 stress 0.5685155
## Run 17 stress 0.5681768
## Run 18 stress 0.551974
## Run 19 stress 0.4774262
## Run 20 stress 0.5683588
## *** No convergence -- monoMDS stopping criteria:
## 6: stress ratio > sratmax
## 14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3729636
## Run 1 stress 0.3877855
## Run 2 stress 0.5686604
## Run 3 stress 0.5671266
## Run 4 stress 0.5598195
## Run 5 stress 0.3828396
## Run 6 stress 0.5335957
## Run 7 stress 0.5679142
## Run 8 stress 0.5394912
## Run 9 stress 0.4413787
## Run 10 stress 0.3837507
## Run 11 stress 0.4048434
## Run 12 stress 0.4202791
## Run 13 stress 0.4811087
## Run 14 stress 0.5538825
## Run 15 stress 0.4360175
## Run 16 stress 0.4666248
## Run 17 stress 0.5452011
## Run 18 stress 0.5685286
## Run 19 stress 0.5684511
## Run 20 stress 0.5681741
## *** No convergence -- monoMDS stopping criteria:
## 4: stress ratio > sratmax
## 16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.361473
## Run 1 stress 0.5674536
## Run 2 stress 0.3705226
## Run 3 stress 0.3665008
## Run 4 stress 0.5251432
## Run 5 stress 0.4795206
## Run 6 stress 0.4343672
## Run 7 stress 0.487786
## Run 8 stress 0.5064389
## Run 9 stress 0.491882
## Run 10 stress 0.45107
## Run 11 stress 0.5333318
## Run 12 stress 0.5681508
## Run 13 stress 0.3614506
## ... New best solution
## ... Procrustes: rmse 0.01441586 max resid 0.07417966
## Run 14 stress 0.4489148
## Run 15 stress 0.5034096
## Run 16 stress 0.4313909
## Run 17 stress 0.568115
## Run 18 stress 0.546872
## Run 19 stress 0.568506
## Run 20 stress 0.5682568
## *** No convergence -- monoMDS stopping criteria:
## 5: stress ratio > sratmax
## 15: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3705003
## Run 1 stress 0.5680188
## Run 2 stress 0.4336803
## Run 3 stress 0.5675581
## Run 4 stress 0.5334681
## Run 5 stress 0.4463232
## Run 6 stress 0.5679463
## Run 7 stress 0.4302918
## Run 8 stress 0.5413346
## Run 9 stress 0.5680125
## Run 10 stress 0.5683107
## Run 11 stress 0.5493182
## Run 12 stress 0.5683157
## Run 13 stress 0.4614034
## Run 14 stress 0.4881365
## Run 15 stress 0.5415326
## Run 16 stress 0.5684518
## Run 17 stress 0.5684734
## Run 18 stress 0.4698176
## Run 19 stress 0.5625737
## Run 20 stress 0.5683277
## *** No convergence -- monoMDS stopping criteria:
## 5: stress ratio > sratmax
## 15: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3670519
## Run 1 stress 0.4452887
## Run 2 stress 0.5521815
## Run 3 stress 0.5034962
## Run 4 stress 0.5373903
## Run 5 stress 0.5680686
## Run 6 stress 0.5678935
## Run 7 stress 0.5650486
## Run 8 stress 0.5031836
## Run 9 stress 0.5654533
## Run 10 stress 0.5683615
## Run 11 stress 0.5680942
## Run 12 stress 0.567856
## Run 13 stress 0.4923205
## Run 14 stress 0.5681236
## Run 15 stress 0.5678589
## Run 16 stress 0.5685633
## Run 17 stress 0.5684371
## Run 18 stress 0.487241
## Run 19 stress 0.4634158
## Run 20 stress 0.4784426
## *** No convergence -- monoMDS stopping criteria:
## 6: stress ratio > sratmax
## 14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3450386
## Run 1 stress 0.344485
## ... New best solution
## ... Procrustes: rmse 0.01417213 max resid 0.09609239
## Run 2 stress 0.5684687
## Run 3 stress 0.3826649
## Run 4 stress 0.5679463
## Run 5 stress 0.5683152
## Run 6 stress 0.4620363
## Run 7 stress 0.5675596
## Run 8 stress 0.4737062
## Run 9 stress 0.5243276
## Run 10 stress 0.4159715
## Run 11 stress 0.3449435
## ... Procrustes: rmse 0.01669781 max resid 0.1162279
## Run 12 stress 0.4699551
## Run 13 stress 0.4732501
## Run 14 stress 0.5681595
## Run 15 stress 0.450047
## Run 16 stress 0.5247535
## Run 17 stress 0.4594415
## Run 18 stress 0.348426
## Run 19 stress 0.4646784
## Run 20 stress 0.3445707
## ... Procrustes: rmse 0.003324356 max resid 0.01258696
## *** No convergence -- monoMDS stopping criteria:
## 7: stress ratio > sratmax
## 13: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3362906
## Run 1 stress 0.5641808
## Run 2 stress 0.4483219
## Run 3 stress 0.3689247
## Run 4 stress 0.4147439
## Run 5 stress 0.4991684
## Run 6 stress 0.481518
## Run 7 stress 0.5679456
## Run 8 stress 0.550369
## Run 9 stress 0.3682479
## Run 10 stress 0.4711453
## Run 11 stress 0.4392174
## Run 12 stress 0.5682475
## Run 13 stress 0.4684234
## Run 14 stress 0.5684503
## Run 15 stress 0.5682988
## Run 16 stress 0.5651844
## Run 17 stress 0.3477934
## Run 18 stress 0.5000595
## Run 19 stress 0.4544496
## Run 20 stress 0.5615737
## *** No convergence -- monoMDS stopping criteria:
## 4: stress ratio > sratmax
## 16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3765862
## Run 1 stress 0.5682679
## Run 2 stress 0.46348
## Run 3 stress 0.5684387
## Run 4 stress 0.5684219
## Run 5 stress 0.5631206
## Run 6 stress 0.4638351
## Run 7 stress 0.5678059
## Run 8 stress 0.4683107
## Run 9 stress 0.4953187
## Run 10 stress 0.476029
## Run 11 stress 0.4563858
## Run 12 stress 0.5685776
## Run 13 stress 0.5682353
## Run 14 stress 0.4950701
## Run 15 stress 0.3935495
## Run 16 stress 0.5138507
## Run 17 stress 0.5686367
## Run 18 stress 0.3890121
## Run 19 stress 0.4923203
## Run 20 stress 0.5672976
## *** No convergence -- monoMDS stopping criteria:
## 5: stress ratio > sratmax
## 15: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.371102
## Run 1 stress 0.5531016
## Run 2 stress 0.4366037
## Run 3 stress 0.5617704
## Run 4 stress 0.5684773
## Run 5 stress 0.5668578
## Run 6 stress 0.4744586
## Run 7 stress 0.482361
## Run 8 stress 0.5169139
## Run 9 stress 0.5442052
## Run 10 stress 0.443081
## Run 11 stress 0.5685282
## Run 12 stress 0.5684348
## Run 13 stress 0.5682799
## Run 14 stress 0.5678955
## Run 15 stress 0.4256311
## Run 16 stress 0.5684209
## Run 17 stress 0.5273724
## Run 18 stress 0.4855864
## Run 19 stress 0.5679672
## Run 20 stress 0.5681544
## *** No convergence -- monoMDS stopping criteria:
## 7: stress ratio > sratmax
## 13: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.359256
## Run 1 stress 0.4813914
## Run 2 stress 0.5461467
## Run 3 stress 0.4848979
## Run 4 stress 0.4134307
## Run 5 stress 0.5384053
## Run 6 stress 0.5655361
## Run 7 stress 0.5273532
## Run 8 stress 0.5679133
## Run 9 stress 0.4187869
## Run 10 stress 0.5675576
## Run 11 stress 0.3590307
## ... New best solution
## ... Procrustes: rmse 0.0152147 max resid 0.07105711
## Run 12 stress 0.5683499
## Run 13 stress 0.5684489
## Run 14 stress 0.4575188
## Run 15 stress 0.4267903
## Run 16 stress 0.568037
## Run 17 stress 0.4140334
## Run 18 stress 0.4273241
## Run 19 stress 0.5453929
## Run 20 stress 0.5686451
## *** No convergence -- monoMDS stopping criteria:
## 7: stress ratio > sratmax
## 13: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3420562
## Run 1 stress 0.467693
## Run 2 stress 0.3429793
## Run 3 stress 0.5684956
## Run 4 stress 0.3607349
## Run 5 stress 0.5672432
## Run 6 stress 0.4975214
## Run 7 stress 0.4188735
## Run 8 stress 0.3748231
## Run 9 stress 0.411328
## Run 10 stress 0.509515
## Run 11 stress 0.3779407
## Run 12 stress 0.384394
## Run 13 stress 0.5682633
## Run 14 stress 0.5677004
## Run 15 stress 0.5684026
## Run 16 stress 0.4033995
## Run 17 stress 0.5685194
## Run 18 stress 0.4015719
## Run 19 stress 0.5682626
## Run 20 stress 0.4931129
## *** No convergence -- monoMDS stopping criteria:
## 3: stress ratio > sratmax
## 17: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3646387
## Run 1 stress 0.5350868
## Run 2 stress 0.4132157
## Run 3 stress 0.5672118
## Run 4 stress 0.4935338
## Run 5 stress 0.4181702
## Run 6 stress 0.568152
## Run 7 stress 0.3648739
## ... Procrustes: rmse 0.004311933 max resid 0.02726331
## Run 8 stress 0.4974078
## Run 9 stress 0.4914274
## Run 10 stress 0.4158754
## Run 11 stress 0.5661599
## Run 12 stress 0.4701289
## Run 13 stress 0.5684419
## Run 14 stress 0.5660656
## Run 15 stress 0.4860794
## Run 16 stress 0.5682188
## Run 17 stress 0.5679819
## Run 18 stress 0.3646933
## ... Procrustes: rmse 0.005048529 max resid 0.01992711
## Run 19 stress 0.5686356
## Run 20 stress 0.5681808
## *** No convergence -- monoMDS stopping criteria:
## 6: stress ratio > sratmax
## 14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3501299
## Run 1 stress 0.5674703
## Run 2 stress 0.5684262
## Run 3 stress 0.5682873
## Run 4 stress 0.3564945
## Run 5 stress 0.5668782
## Run 6 stress 0.5548761
## Run 7 stress 0.4908984
## Run 8 stress 0.5674929
## Run 9 stress 0.5681265
## Run 10 stress 0.5619067
## Run 11 stress 0.5680905
## Run 12 stress 0.5232781
## Run 13 stress 0.3673538
## Run 14 stress 0.5683727
## Run 15 stress 0.4172845
## Run 16 stress 0.4510423
## Run 17 stress 0.5682977
## Run 18 stress 0.5683414
## Run 19 stress 0.5665338
## Run 20 stress 0.4591338
## *** No convergence -- monoMDS stopping criteria:
## 2: stress ratio > sratmax
## 18: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.4032906
## Run 1 stress 0.4106769
## Run 2 stress 0.5683403
## Run 3 stress 0.5678662
## Run 4 stress 0.5684957
## Run 5 stress 0.4250176
## Run 6 stress 0.4191311
## Run 7 stress 0.4427645
## Run 8 stress 0.5677323
## Run 9 stress 0.5686239
## Run 10 stress 0.5680608
## Run 11 stress 0.4286555
## Run 12 stress 0.5685516
## Run 13 stress 0.4791662
## Run 14 stress 0.5684969
## Run 15 stress 0.4572891
## Run 16 stress 0.4517909
## Run 17 stress 0.4630738
## Run 18 stress 0.5686066
## Run 19 stress 0.5686678
## Run 20 stress 0.4448143
## *** No convergence -- monoMDS stopping criteria:
## 3: stress ratio > sratmax
## 17: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1901664
## Run 1 stress 0.5657643
## Run 2 stress 0.5636877
## Run 3 stress 0.1897935
## ... New best solution
## ... Procrustes: rmse 0.008534418 max resid 0.05961287
## Run 4 stress 0.1897189
## ... New best solution
## ... Procrustes: rmse 0.002473722 max resid 0.01098358
## Run 5 stress 0.5685319
## Run 6 stress 0.544491
## Run 7 stress 0.2737205
## Run 8 stress 0.190344
## Run 9 stress 0.4582411
## Run 10 stress 0.1902855
## Run 11 stress 0.510432
## Run 12 stress 0.5624999
## Run 13 stress 0.2765784
## Run 14 stress 0.2755697
## Run 15 stress 0.1899135
## ... Procrustes: rmse 0.003664034 max resid 0.01813173
## Run 16 stress 0.557042
## Run 17 stress 0.5551162
## Run 18 stress 0.5683189
## Run 19 stress 0.1898422
## ... Procrustes: rmse 0.00198652 max resid 0.00995406
## ... Similar to previous best
## Run 20 stress 0.5676039
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1815256
## Run 1 stress 0.1816058
## ... Procrustes: rmse 0.005145445 max resid 0.0373673
## Run 2 stress 0.1824844
## Run 3 stress 0.1824844
## Run 4 stress 0.1819584
## ... Procrustes: rmse 0.03454869 max resid 0.2670509
## Run 5 stress 0.1816064
## ... Procrustes: rmse 0.005138434 max resid 0.03730599
## Run 6 stress 0.1819576
## ... Procrustes: rmse 0.03443718 max resid 0.2669919
## Run 7 stress 0.1819575
## ... Procrustes: rmse 0.03444723 max resid 0.2669882
## Run 8 stress 0.1816058
## ... Procrustes: rmse 0.005130142 max resid 0.03726707
## Run 9 stress 0.1816058
## ... Procrustes: rmse 0.005143062 max resid 0.03735822
## Run 10 stress 0.1815256
## ... New best solution
## ... Procrustes: rmse 2.011378e-05 max resid 8.165248e-05
## ... Similar to previous best
## Run 11 stress 0.1824965
## Run 12 stress 0.1819577
## ... Procrustes: rmse 0.03443266 max resid 0.2669996
## Run 13 stress 0.1815257
## ... Procrustes: rmse 6.470238e-05 max resid 0.0003762505
## ... Similar to previous best
## Run 14 stress 0.1833
## Run 15 stress 0.1816059
## ... Procrustes: rmse 0.005137459 max resid 0.0373192
## Run 16 stress 0.1819578
## ... Procrustes: rmse 0.03450049 max resid 0.2670379
## Run 17 stress 0.1815257
## ... Procrustes: rmse 8.186038e-05 max resid 0.0004277621
## ... Similar to previous best
## Run 18 stress 0.181606
## ... Procrustes: rmse 0.005150956 max resid 0.03740907
## Run 19 stress 0.2056097
## Run 20 stress 0.1824844
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1896778
## Run 1 stress 0.1884253
## ... New best solution
## ... Procrustes: rmse 0.02282997 max resid 0.1761241
## Run 2 stress 0.2004506
## Run 3 stress 0.1914619
## Run 4 stress 0.2005318
## Run 5 stress 0.1891668
## Run 6 stress 0.1893407
## Run 7 stress 0.2321239
## Run 8 stress 0.1904069
## Run 9 stress 0.1884426
## ... Procrustes: rmse 0.002276795 max resid 0.01437376
## Run 10 stress 0.1888497
## ... Procrustes: rmse 0.0114335 max resid 0.08532459
## Run 11 stress 0.2005318
## Run 12 stress 0.1893411
## Run 13 stress 0.1914768
## Run 14 stress 0.2005317
## Run 15 stress 0.1889407
## Run 16 stress 0.1904066
## Run 17 stress 0.1884469
## ... Procrustes: rmse 0.02907987 max resid 0.1875463
## Run 18 stress 0.1884446
## ... Procrustes: rmse 0.02922003 max resid 0.1879458
## Run 19 stress 0.18885
## ... Procrustes: rmse 0.01151651 max resid 0.08603751
## Run 20 stress 0.1891666
## *** No convergence -- monoMDS stopping criteria:
## 19: stress ratio > sratmax
## 1: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1864124
## Run 1 stress 0.1911627
## Run 2 stress 0.2163852
## Run 3 stress 0.1840202
## ... New best solution
## ... Procrustes: rmse 0.03594734 max resid 0.2294318
## Run 4 stress 0.1865746
## Run 5 stress 0.1958795
## Run 6 stress 0.2089148
## Run 7 stress 0.1869208
## Run 8 stress 0.1844912
## ... Procrustes: rmse 0.01940025 max resid 0.0783345
## Run 9 stress 0.1840013
## ... New best solution
## ... Procrustes: rmse 0.005212787 max resid 0.02364139
## Run 10 stress 0.2190791
## Run 11 stress 0.406593
## Run 12 stress 0.184378
## ... Procrustes: rmse 0.01776723 max resid 0.08400709
## Run 13 stress 0.1911629
## Run 14 stress 0.1921569
## Run 15 stress 0.1911629
## Run 16 stress 0.1926636
## Run 17 stress 0.203463
## Run 18 stress 0.1921569
## Run 19 stress 0.1926629
## Run 20 stress 0.1958946
## *** No convergence -- monoMDS stopping criteria:
## 20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.187465
## Run 1 stress 0.2105465
## Run 2 stress 0.1875618
## ... Procrustes: rmse 0.003730648 max resid 0.02466595
## Run 3 stress 0.2326598
## Run 4 stress 0.1875618
## ... Procrustes: rmse 0.003717748 max resid 0.02457644
## Run 5 stress 0.1875527
## ... Procrustes: rmse 0.01029553 max resid 0.07257547
## Run 6 stress 0.1875527
## ... Procrustes: rmse 0.01029144 max resid 0.07255269
## Run 7 stress 0.1875527
## ... Procrustes: rmse 0.01029292 max resid 0.07256231
## Run 8 stress 0.2095598
## Run 9 stress 0.2105465
## Run 10 stress 0.1875527
## ... Procrustes: rmse 0.0102898 max resid 0.07254486
## Run 11 stress 0.2066865
## Run 12 stress 0.2312508
## Run 13 stress 0.1875625
## ... Procrustes: rmse 0.003884934 max resid 0.02582226
## Run 14 stress 0.1875527
## ... Procrustes: rmse 0.01030238 max resid 0.07263194
## Run 15 stress 0.1875527
## ... Procrustes: rmse 0.01029361 max resid 0.07256713
## Run 16 stress 0.1875527
## ... Procrustes: rmse 0.01028975 max resid 0.0725293
## Run 17 stress 0.1875618
## ... Procrustes: rmse 0.003719725 max resid 0.02454185
## Run 18 stress 0.2105466
## Run 19 stress 0.2096271
## Run 20 stress 0.2066864
## *** No convergence -- monoMDS stopping criteria:
## 19: stress ratio > sratmax
## 1: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1821758
## Run 1 stress 0.1879531
## Run 2 stress 0.1877436
## Run 3 stress 0.1877651
## Run 4 stress 0.190829
## Run 5 stress 0.1871566
## Run 6 stress 0.1878673
## Run 7 stress 0.196424
## Run 8 stress 0.1871566
## Run 9 stress 0.1997363
## Run 10 stress 0.2106503
## Run 11 stress 0.182137
## ... New best solution
## ... Procrustes: rmse 0.005806067 max resid 0.04203009
## Run 12 stress 0.1899351
## Run 13 stress 0.2008168
## Run 14 stress 0.1949076
## Run 15 stress 0.1871502
## Run 16 stress 0.1939492
## Run 17 stress 0.182636
## ... Procrustes: rmse 0.00971831 max resid 0.0550377
## Run 18 stress 0.1879534
## Run 19 stress 0.1899244
## Run 20 stress 0.1915868
## *** No convergence -- monoMDS stopping criteria:
## 19: stress ratio > sratmax
## 1: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1728594
## Run 1 stress 0.1727911
## ... New best solution
## ... Procrustes: rmse 0.006041499 max resid 0.03799394
## Run 2 stress 0.1727719
## ... New best solution
## ... Procrustes: rmse 0.002102114 max resid 0.0136238
## Run 3 stress 0.1727697
## ... New best solution
## ... Procrustes: rmse 0.0003959877 max resid 0.002702283
## ... Similar to previous best
## Run 4 stress 0.1727699
## ... Procrustes: rmse 5.972941e-05 max resid 0.0003625102
## ... Similar to previous best
## Run 5 stress 0.1731677
## ... Procrustes: rmse 0.008687875 max resid 0.0403693
## Run 6 stress 0.1832575
## Run 7 stress 0.1727694
## ... New best solution
## ... Procrustes: rmse 0.000182532 max resid 0.001166911
## ... Similar to previous best
## Run 8 stress 0.1728555
## ... Procrustes: rmse 0.005962931 max resid 0.03793635
## Run 9 stress 0.1731678
## ... Procrustes: rmse 0.008627619 max resid 0.04013339
## Run 10 stress 0.1832579
## Run 11 stress 0.1727697
## ... Procrustes: rmse 0.000162877 max resid 0.001067674
## ... Similar to previous best
## Run 12 stress 0.1731678
## ... Procrustes: rmse 0.008629405 max resid 0.04012422
## Run 13 stress 0.1728597
## ... Procrustes: rmse 0.006711308 max resid 0.03906967
## Run 14 stress 0.1727697
## ... Procrustes: rmse 0.0001688499 max resid 0.001102657
## ... Similar to previous best
## Run 15 stress 0.1727741
## ... Procrustes: rmse 0.0007430364 max resid 0.004973579
## ... Similar to previous best
## Run 16 stress 0.172773
## ... Procrustes: rmse 0.0007127333 max resid 0.004845445
## ... Similar to previous best
## Run 17 stress 0.1728564
## ... Procrustes: rmse 0.00593131 max resid 0.03790944
## Run 18 stress 0.183258
## Run 19 stress 0.1728594
## ... Procrustes: rmse 0.006705524 max resid 0.03903445
## Run 20 stress 0.1727694
## ... Procrustes: rmse 5.037598e-05 max resid 0.0003046885
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1742136
## Run 1 stress 0.1742393
## ... Procrustes: rmse 0.002056202 max resid 0.01131298
## Run 2 stress 0.1742426
## ... Procrustes: rmse 0.002093411 max resid 0.01135176
## Run 3 stress 0.1742434
## ... Procrustes: rmse 0.002221983 max resid 0.01127869
## Run 4 stress 0.1742153
## ... Procrustes: rmse 0.002169998 max resid 0.01114556
## Run 5 stress 0.2178045
## Run 6 stress 0.2127924
## Run 7 stress 0.1742318
## ... Procrustes: rmse 0.001790808 max resid 0.01115193
## Run 8 stress 0.2175262
## Run 9 stress 0.2352813
## Run 10 stress 0.2132001
## Run 11 stress 0.1742384
## ... Procrustes: rmse 0.002054161 max resid 0.01125592
## Run 12 stress 0.1742206
## ... Procrustes: rmse 0.0006144124 max resid 0.003465283
## ... Similar to previous best
## Run 13 stress 0.1742303
## ... Procrustes: rmse 0.001780432 max resid 0.01112403
## Run 14 stress 0.1742857
## ... Procrustes: rmse 0.004320328 max resid 0.02357573
## Run 15 stress 0.1742399
## ... Procrustes: rmse 0.002124847 max resid 0.01128626
## Run 16 stress 0.17423
## ... Procrustes: rmse 0.001776036 max resid 0.01111521
## Run 17 stress 0.1742345
## ... Procrustes: rmse 0.001885097 max resid 0.01118258
## Run 18 stress 0.2149854
## Run 19 stress 0.174545
## ... Procrustes: rmse 0.007105394 max resid 0.04009053
## Run 20 stress 0.2019257
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1864509
## Run 1 stress 0.1866276
## ... Procrustes: rmse 0.003944203 max resid 0.02499313
## Run 2 stress 0.1967001
## Run 3 stress 0.1871682
## Run 4 stress 0.1866296
## ... Procrustes: rmse 0.008930746 max resid 0.04334465
## Run 5 stress 0.1876463
## Run 6 stress 0.1872107
## Run 7 stress 0.1965815
## Run 8 stress 0.1865067
## ... Procrustes: rmse 0.001841989 max resid 0.01072541
## Run 9 stress 0.18663
## ... Procrustes: rmse 0.009072128 max resid 0.04448871
## Run 10 stress 0.1866296
## ... Procrustes: rmse 0.008887181 max resid 0.0430039
## Run 11 stress 0.1866296
## ... Procrustes: rmse 0.00890705 max resid 0.04315848
## Run 12 stress 0.1866299
## ... Procrustes: rmse 0.00904365 max resid 0.04426748
## Run 13 stress 0.1872109
## Run 14 stress 0.186681
## ... Procrustes: rmse 0.009235142 max resid 0.04419763
## Run 15 stress 0.2334132
## Run 16 stress 0.2541016
## Run 17 stress 0.186884
## ... Procrustes: rmse 0.009725193 max resid 0.04274832
## Run 18 stress 0.1967021
## Run 19 stress 0.1869915
## Run 20 stress 0.1866296
## ... Procrustes: rmse 0.008944563 max resid 0.04346556
## *** No convergence -- monoMDS stopping criteria:
## 1: no. of iterations >= maxit
## 19: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1891473
## Run 1 stress 0.4066248
## Run 2 stress 0.1870536
## ... New best solution
## ... Procrustes: rmse 0.02830164 max resid 0.169005
## Run 3 stress 0.191121
## Run 4 stress 0.1894983
## Run 5 stress 0.1870538
## ... Procrustes: rmse 0.0001845659 max resid 0.001202453
## ... Similar to previous best
## Run 6 stress 0.1909159
## Run 7 stress 0.2097651
## Run 8 stress 0.1870539
## ... Procrustes: rmse 7.659384e-05 max resid 0.000410041
## ... Similar to previous best
## Run 9 stress 0.1870541
## ... Procrustes: rmse 0.0003113738 max resid 0.002109818
## ... Similar to previous best
## Run 10 stress 0.1909185
## Run 11 stress 0.205467
## Run 12 stress 0.1930387
## Run 13 stress 0.1909159
## Run 14 stress 0.2036172
## Run 15 stress 0.2073884
## Run 16 stress 0.1915624
## Run 17 stress 0.1868665
## ... New best solution
## ... Procrustes: rmse 0.007748254 max resid 0.04610815
## Run 18 stress 0.1868664
## ... New best solution
## ... Procrustes: rmse 4.753065e-05 max resid 0.0002095712
## ... Similar to previous best
## Run 19 stress 0.1870541
## ... Procrustes: rmse 0.007880155 max resid 0.04633346
## Run 20 stress 0.1891004
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1770762
## Run 1 stress 0.1770825
## ... Procrustes: rmse 0.0008693537 max resid 0.003943071
## ... Similar to previous best
## Run 2 stress 0.17977
## Run 3 stress 0.1770812
## ... Procrustes: rmse 0.0007404488 max resid 0.003901623
## ... Similar to previous best
## Run 4 stress 0.1839565
## Run 5 stress 0.1839564
## Run 6 stress 0.1839564
## Run 7 stress 0.1770822
## ... Procrustes: rmse 0.0008474877 max resid 0.003938287
## ... Similar to previous best
## Run 8 stress 0.1818929
## Run 9 stress 0.1839564
## Run 10 stress 0.1770762
## ... New best solution
## ... Procrustes: rmse 3.198938e-05 max resid 0.0001415899
## ... Similar to previous best
## Run 11 stress 0.177076
## ... New best solution
## ... Procrustes: rmse 6.643889e-05 max resid 0.0002459714
## ... Similar to previous best
## Run 12 stress 0.1770761
## ... Procrustes: rmse 3.215675e-05 max resid 0.0001751725
## ... Similar to previous best
## Run 13 stress 0.181769
## Run 14 stress 0.177076
## ... New best solution
## ... Procrustes: rmse 2.260129e-05 max resid 0.0001008824
## ... Similar to previous best
## Run 15 stress 0.1770806
## ... Procrustes: rmse 0.0006355951 max resid 0.003847123
## ... Similar to previous best
## Run 16 stress 0.1770807
## ... Procrustes: rmse 0.0006630747 max resid 0.003864112
## ... Similar to previous best
## Run 17 stress 0.1797698
## Run 18 stress 0.1839564
## Run 19 stress 0.1839566
## Run 20 stress 0.1770809
## ... Procrustes: rmse 0.0006493665 max resid 0.003851454
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1782136
## Run 1 stress 0.1784765
## ... Procrustes: rmse 0.006084041 max resid 0.03697257
## Run 2 stress 0.1782136
## ... New best solution
## ... Procrustes: rmse 1.354728e-05 max resid 6.754975e-05
## ... Similar to previous best
## Run 3 stress 0.1782313
## ... Procrustes: rmse 0.003424529 max resid 0.02540403
## Run 4 stress 0.1782103
## ... New best solution
## ... Procrustes: rmse 0.0007471869 max resid 0.004407587
## ... Similar to previous best
## Run 5 stress 0.1782103
## ... Procrustes: rmse 0.0001272564 max resid 0.0008859291
## ... Similar to previous best
## Run 6 stress 0.2234971
## Run 7 stress 0.4066402
## Run 8 stress 0.1782136
## ... Procrustes: rmse 0.0007490621 max resid 0.004416154
## ... Similar to previous best
## Run 9 stress 0.1782103
## ... Procrustes: rmse 9.423713e-05 max resid 0.0006417563
## ... Similar to previous best
## Run 10 stress 0.1782105
## ... Procrustes: rmse 0.0001340003 max resid 0.000896655
## ... Similar to previous best
## Run 11 stress 0.1784774
## ... Procrustes: rmse 0.005999608 max resid 0.03669724
## Run 12 stress 0.1813525
## Run 13 stress 0.1782103
## ... Procrustes: rmse 7.825216e-05 max resid 0.0005463202
## ... Similar to previous best
## Run 14 stress 0.1782103
## ... Procrustes: rmse 0.000102705 max resid 0.0007174098
## ... Similar to previous best
## Run 15 stress 0.1782136
## ... Procrustes: rmse 0.0007491371 max resid 0.004412754
## ... Similar to previous best
## Run 16 stress 0.1782282
## ... Procrustes: rmse 0.003416444 max resid 0.02535108
## Run 17 stress 0.1784768
## ... Procrustes: rmse 0.006240043 max resid 0.03728032
## Run 18 stress 0.1782136
## ... Procrustes: rmse 0.0007472772 max resid 0.004408359
## ... Similar to previous best
## Run 19 stress 0.1784768
## ... Procrustes: rmse 0.006240445 max resid 0.037284
## Run 20 stress 0.1782137
## ... Procrustes: rmse 0.0007594819 max resid 0.004414149
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1779773
## Run 1 stress 0.1781438
## ... Procrustes: rmse 0.01074618 max resid 0.0748357
## Run 2 stress 0.1972246
## Run 3 stress 0.1779772
## ... New best solution
## ... Procrustes: rmse 0.0002839653 max resid 0.001521159
## ... Similar to previous best
## Run 4 stress 0.2091888
## Run 5 stress 0.1781434
## ... Procrustes: rmse 0.01045016 max resid 0.07399386
## Run 6 stress 0.1781435
## ... Procrustes: rmse 0.01060859 max resid 0.07467526
## Run 7 stress 0.1819159
## Run 8 stress 0.1779216
## ... New best solution
## ... Procrustes: rmse 0.004928058 max resid 0.03036705
## Run 9 stress 0.17972
## Run 10 stress 0.2092
## Run 11 stress 0.1797221
## Run 12 stress 0.1808562
## Run 13 stress 0.1808562
## Run 14 stress 0.178147
## ... Procrustes: rmse 0.01392132 max resid 0.104108
## Run 15 stress 0.1797193
## Run 16 stress 0.2263344
## Run 17 stress 0.1808584
## Run 18 stress 0.1819326
## Run 19 stress 0.1908401
## Run 20 stress 0.180857
## *** No convergence -- monoMDS stopping criteria:
## 20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.2141035
## Run 1 stress 0.2173049
## Run 2 stress 0.2130141
## ... New best solution
## ... Procrustes: rmse 0.03280388 max resid 0.1798519
## Run 3 stress 0.2144367
## Run 4 stress 0.2290151
## Run 5 stress 0.2130785
## ... Procrustes: rmse 0.005693901 max resid 0.0361183
## Run 6 stress 0.2157648
## Run 7 stress 0.2274414
## Run 8 stress 0.2183311
## Run 9 stress 0.2130153
## ... Procrustes: rmse 0.0005059794 max resid 0.003176342
## ... Similar to previous best
## Run 10 stress 0.2130169
## ... Procrustes: rmse 0.0007227888 max resid 0.004301562
## ... Similar to previous best
## Run 11 stress 0.2130178
## ... Procrustes: rmse 0.0008817058 max resid 0.005768768
## ... Similar to previous best
## Run 12 stress 0.2224566
## Run 13 stress 0.2290861
## Run 14 stress 0.2316146
## Run 15 stress 0.2178871
## Run 16 stress 0.2301753
## Run 17 stress 0.2487429
## Run 18 stress 0.2145932
## Run 19 stress 0.2185976
## Run 20 stress 0.2290861
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1950622
## Run 1 stress 0.4072655
## Run 2 stress 0.1964355
## Run 3 stress 0.19505
## ... New best solution
## ... Procrustes: rmse 0.02041892 max resid 0.1523433
## Run 4 stress 0.203728
## Run 5 stress 0.2093407
## Run 6 stress 0.1950622
## ... Procrustes: rmse 0.02047519 max resid 0.1527665
## Run 7 stress 0.1971281
## Run 8 stress 0.1950501
## ... Procrustes: rmse 9.963248e-05 max resid 0.0006720585
## ... Similar to previous best
## Run 9 stress 0.1964738
## Run 10 stress 0.2238816
## Run 11 stress 0.19505
## ... Procrustes: rmse 1.307048e-05 max resid 6.094718e-05
## ... Similar to previous best
## Run 12 stress 0.1964353
## Run 13 stress 0.1970423
## Run 14 stress 0.1964743
## Run 15 stress 0.2037287
## Run 16 stress 0.1971294
## Run 17 stress 0.19505
## ... Procrustes: rmse 1.925538e-05 max resid 0.0001062048
## ... Similar to previous best
## Run 18 stress 0.2093301
## Run 19 stress 0.197046
## Run 20 stress 0.2150376
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.197
## Run 1 stress 0.1976006
## Run 2 stress 0.2040656
## Run 3 stress 0.1970012
## ... Procrustes: rmse 0.0002339557 max resid 0.001117705
## ... Similar to previous best
## Run 4 stress 0.2181836
## Run 5 stress 0.1976408
## Run 6 stress 0.2024077
## Run 7 stress 0.2042805
## Run 8 stress 0.1977643
## Run 9 stress 0.1979196
## Run 10 stress 0.1977643
## Run 11 stress 0.1979197
## Run 12 stress 0.1986713
## Run 13 stress 0.2151953
## Run 14 stress 0.2025296
## Run 15 stress 0.1977647
## Run 16 stress 0.2173611
## Run 17 stress 0.1986427
## Run 18 stress 0.2051211
## Run 19 stress 0.1975449
## Run 20 stress 0.2046347
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1935637
## Run 1 stress 0.1935442
## ... New best solution
## ... Procrustes: rmse 0.001799763 max resid 0.01041083
## Run 2 stress 0.1924876
## ... New best solution
## ... Procrustes: rmse 0.03160737 max resid 0.131905
## Run 3 stress 0.1935625
## Run 4 stress 0.1967101
## Run 5 stress 0.1958003
## Run 6 stress 0.1961546
## Run 7 stress 0.1935643
## Run 8 stress 0.1960476
## Run 9 stress 0.1942672
## Run 10 stress 0.1967443
## Run 11 stress 0.2378625
## Run 12 stress 0.1925342
## ... Procrustes: rmse 0.02800754 max resid 0.1284411
## Run 13 stress 0.1965406
## Run 14 stress 0.1957997
## Run 15 stress 0.1960145
## Run 16 stress 0.1960143
## Run 17 stress 0.1935443
## Run 18 stress 0.201235
## Run 19 stress 0.1983769
## Run 20 stress 0.2012492
## *** No convergence -- monoMDS stopping criteria:
## 20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1824375
## Run 1 stress 0.1824375
## ... New best solution
## ... Procrustes: rmse 1.183988e-05 max resid 7.819541e-05
## ... Similar to previous best
## Run 2 stress 0.1799002
## ... New best solution
## ... Procrustes: rmse 0.03638419 max resid 0.2833504
## Run 3 stress 0.1802371
## ... Procrustes: rmse 0.01568607 max resid 0.1187144
## Run 4 stress 0.1824375
## Run 5 stress 0.1799164
## ... Procrustes: rmse 0.001152904 max resid 0.006458535
## ... Similar to previous best
## Run 6 stress 0.1798997
## ... New best solution
## ... Procrustes: rmse 0.000924637 max resid 0.005496584
## ... Similar to previous best
## Run 7 stress 0.1802375
## ... Procrustes: rmse 0.01591901 max resid 0.1203792
## Run 8 stress 0.180238
## ... Procrustes: rmse 0.01559536 max resid 0.117611
## Run 9 stress 0.1799065
## ... Procrustes: rmse 0.001087964 max resid 0.005780038
## ... Similar to previous best
## Run 10 stress 0.1827093
## Run 11 stress 0.1799
## ... Procrustes: rmse 7.934643e-05 max resid 0.0004375639
## ... Similar to previous best
## Run 12 stress 0.1824375
## Run 13 stress 0.1798999
## ... Procrustes: rmse 7.35966e-05 max resid 0.0004380104
## ... Similar to previous best
## Run 14 stress 0.180237
## ... Procrustes: rmse 0.0158574 max resid 0.1197689
## Run 15 stress 0.182784
## Run 16 stress 0.1799163
## ... Procrustes: rmse 0.001755132 max resid 0.007146625
## ... Similar to previous best
## Run 17 stress 0.1799134
## ... Procrustes: rmse 0.001493537 max resid 0.006323934
## ... Similar to previous best
## Run 18 stress 0.1798996
## ... New best solution
## ... Procrustes: rmse 0.0008734725 max resid 0.005340798
## ... Similar to previous best
## Run 19 stress 0.182784
## Run 20 stress 0.1799
## ... Procrustes: rmse 0.0007796546 max resid 0.004751483
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1945802
## Run 1 stress 0.2021536
## Run 2 stress 0.2004611
## Run 3 stress 0.194604
## ... Procrustes: rmse 0.01156539 max resid 0.04097248
## Run 4 stress 0.1947028
## ... Procrustes: rmse 0.00769767 max resid 0.03726731
## Run 5 stress 0.2004504
## Run 6 stress 0.2021535
## Run 7 stress 0.1945791
## ... New best solution
## ... Procrustes: rmse 0.008331195 max resid 0.03837592
## Run 8 stress 0.2090408
## Run 9 stress 0.2215714
## Run 10 stress 0.1947029
## ... Procrustes: rmse 0.00988 max resid 0.03513249
## Run 11 stress 0.2019956
## Run 12 stress 0.1946038
## ... Procrustes: rmse 0.006979456 max resid 0.0364319
## Run 13 stress 0.1946664
## ... Procrustes: rmse 0.005119146 max resid 0.03556831
## Run 14 stress 0.1948184
## ... Procrustes: rmse 0.01456816 max resid 0.09094829
## Run 15 stress 0.2195094
## Run 16 stress 0.1946657
## ... Procrustes: rmse 0.0150406 max resid 0.09210628
## Run 17 stress 0.223662
## Run 18 stress 0.2125449
## Run 19 stress 0.1944898
## ... New best solution
## ... Procrustes: rmse 0.00684143 max resid 0.03219302
## Run 20 stress 0.1946038
## ... Procrustes: rmse 0.007601894 max resid 0.03902079
## *** No convergence -- monoMDS stopping criteria:
## 20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1905614
## Run 1 stress 0.1959151
## Run 2 stress 0.2171768
## Run 3 stress 0.2242984
## Run 4 stress 0.1959211
## Run 5 stress 0.2271224
## Run 6 stress 0.1920407
## Run 7 stress 0.1905913
## ... Procrustes: rmse 0.0027797 max resid 0.01887006
## Run 8 stress 0.1905595
## ... New best solution
## ... Procrustes: rmse 0.004425766 max resid 0.02283778
## Run 9 stress 0.192044
## Run 10 stress 0.1959157
## Run 11 stress 0.1920442
## Run 12 stress 0.2254135
## Run 13 stress 0.1903248
## ... New best solution
## ... Procrustes: rmse 0.007841821 max resid 0.04473863
## Run 14 stress 0.1903248
## ... Procrustes: rmse 4.338024e-05 max resid 0.0002875893
## ... Similar to previous best
## Run 15 stress 0.2153495
## Run 16 stress 0.1920431
## Run 17 stress 0.1920456
## Run 18 stress 0.229066
## Run 19 stress 0.2165586
## Run 20 stress 0.1959181
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.2063212
## Run 1 stress 0.2090702
## Run 2 stress 0.2080069
## Run 3 stress 0.2090699
## Run 4 stress 0.2488213
## Run 5 stress 0.2090611
## Run 6 stress 0.2063188
## ... New best solution
## ... Procrustes: rmse 0.0004045549 max resid 0.001698455
## ... Similar to previous best
## Run 7 stress 0.2534538
## Run 8 stress 0.2080069
## Run 9 stress 0.2090698
## Run 10 stress 0.236734
## Run 11 stress 0.4077266
## Run 12 stress 0.2090699
## Run 13 stress 0.2083877
## Run 14 stress 0.2090699
## Run 15 stress 0.20907
## Run 16 stress 0.212576
## Run 17 stress 0.2083428
## Run 18 stress 0.2063195
## ... Procrustes: rmse 0.0002972807 max resid 0.001275668
## ... Similar to previous best
## Run 19 stress 0.2090698
## Run 20 stress 0.2083444
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0762502
## Run 1 stress 0.07625021
## ... Procrustes: rmse 1.366488e-05 max resid 7.766714e-05
## ... Similar to previous best
## Run 2 stress 0.08614381
## Run 3 stress 0.07130037
## ... New best solution
## ... Procrustes: rmse 0.03267107 max resid 0.2604145
## Run 4 stress 0.0762502
## Run 5 stress 0.1132713
## Run 6 stress 0.1046431
## Run 7 stress 0.08193687
## Run 8 stress 0.08619594
## Run 9 stress 0.08614369
## Run 10 stress 0.1324131
## Run 11 stress 0.0861957
## Run 12 stress 0.0762503
## Run 13 stress 0.07625028
## Run 14 stress 0.12416
## Run 15 stress 0.08193689
## Run 16 stress 0.07625021
## Run 17 stress 0.08194626
## Run 18 stress 0.0762502
## Run 19 stress 0.08619573
## Run 20 stress 0.0762502
## *** No convergence -- monoMDS stopping criteria:
## 17: stress ratio > sratmax
## 3: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08481971
## Run 1 stress 0.08482014
## ... Procrustes: rmse 0.001897914 max resid 0.01270675
## Run 2 stress 0.08481768
## ... New best solution
## ... Procrustes: rmse 0.0002494052 max resid 0.001559841
## ... Similar to previous best
## Run 3 stress 0.08482271
## ... Procrustes: rmse 0.0005148402 max resid 0.003243802
## ... Similar to previous best
## Run 4 stress 0.08481903
## ... Procrustes: rmse 0.00151954 max resid 0.01026913
## Run 5 stress 0.084822
## ... Procrustes: rmse 0.0003808411 max resid 0.002010741
## ... Similar to previous best
## Run 6 stress 0.08481975
## ... Procrustes: rmse 0.0002191837 max resid 0.001331836
## ... Similar to previous best
## Run 7 stress 0.08481655
## ... New best solution
## ... Procrustes: rmse 0.001201592 max resid 0.008103075
## ... Similar to previous best
## Run 8 stress 0.08481897
## ... Procrustes: rmse 0.001330943 max resid 0.008982136
## ... Similar to previous best
## Run 9 stress 0.0848221
## ... Procrustes: rmse 0.0006232144 max resid 0.004216975
## ... Similar to previous best
## Run 10 stress 0.08481864
## ... Procrustes: rmse 0.001342561 max resid 0.008996008
## ... Similar to previous best
## Run 11 stress 0.08481786
## ... Procrustes: rmse 0.0008374444 max resid 0.004469169
## ... Similar to previous best
## Run 12 stress 0.08482044
## ... Procrustes: rmse 0.001536888 max resid 0.01024284
## Run 13 stress 0.08481867
## ... Procrustes: rmse 0.001358826 max resid 0.009027846
## ... Similar to previous best
## Run 14 stress 0.08481631
## ... New best solution
## ... Procrustes: rmse 0.0008047481 max resid 0.004316925
## ... Similar to previous best
## Run 15 stress 0.08481928
## ... Procrustes: rmse 0.0007265349 max resid 0.005143873
## ... Similar to previous best
## Run 16 stress 0.08482282
## ... Procrustes: rmse 0.001448681 max resid 0.009072121
## ... Similar to previous best
## Run 17 stress 0.08482621
## ... Procrustes: rmse 0.001604087 max resid 0.009898067
## ... Similar to previous best
## Run 18 stress 0.08482233
## ... Procrustes: rmse 0.0008876703 max resid 0.006285566
## ... Similar to previous best
## Run 19 stress 0.08481895
## ... Procrustes: rmse 0.001106423 max resid 0.006547255
## ... Similar to previous best
## Run 20 stress 0.08481606
## ... New best solution
## ... Procrustes: rmse 0.0007222563 max resid 0.003686685
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0835775
## Run 1 stress 0.08357751
## ... Procrustes: rmse 3.081082e-05 max resid 0.0001271349
## ... Similar to previous best
## Run 2 stress 0.08357766
## ... Procrustes: rmse 9.659152e-05 max resid 0.0005146427
## ... Similar to previous best
## Run 3 stress 0.0835775
## ... New best solution
## ... Procrustes: rmse 1.955098e-05 max resid 7.635037e-05
## ... Similar to previous best
## Run 4 stress 0.08357754
## ... Procrustes: rmse 3.850813e-05 max resid 0.0002230852
## ... Similar to previous best
## Run 5 stress 0.08357751
## ... Procrustes: rmse 3.373048e-05 max resid 0.0001454563
## ... Similar to previous best
## Run 6 stress 0.08357762
## ... Procrustes: rmse 2.46504e-05 max resid 0.0001157568
## ... Similar to previous best
## Run 7 stress 0.08357753
## ... Procrustes: rmse 3.541417e-05 max resid 0.0002424505
## ... Similar to previous best
## Run 8 stress 0.08357754
## ... Procrustes: rmse 5.146239e-05 max resid 0.0002249132
## ... Similar to previous best
## Run 9 stress 0.08357752
## ... Procrustes: rmse 2.696773e-05 max resid 0.0001761893
## ... Similar to previous best
## Run 10 stress 0.0835775
## ... New best solution
## ... Procrustes: rmse 8.74367e-06 max resid 4.559658e-05
## ... Similar to previous best
## Run 11 stress 0.0835775
## ... Procrustes: rmse 1.661321e-05 max resid 7.599255e-05
## ... Similar to previous best
## Run 12 stress 0.08357772
## ... Procrustes: rmse 0.0001061425 max resid 0.000466474
## ... Similar to previous best
## Run 13 stress 0.0835775
## ... New best solution
## ... Procrustes: rmse 6.156195e-06 max resid 3.971743e-05
## ... Similar to previous best
## Run 14 stress 0.0835775
## ... Procrustes: rmse 2.189526e-05 max resid 9.64143e-05
## ... Similar to previous best
## Run 15 stress 0.0835775
## ... Procrustes: rmse 1.618422e-05 max resid 9.460451e-05
## ... Similar to previous best
## Run 16 stress 0.0835775
## ... Procrustes: rmse 7.934605e-06 max resid 2.559633e-05
## ... Similar to previous best
## Run 17 stress 0.0835775
## ... Procrustes: rmse 9.436833e-06 max resid 4.275371e-05
## ... Similar to previous best
## Run 18 stress 0.08357762
## ... Procrustes: rmse 3.708843e-05 max resid 0.0001408645
## ... Similar to previous best
## Run 19 stress 0.0835775
## ... Procrustes: rmse 8.050846e-06 max resid 2.949371e-05
## ... Similar to previous best
## Run 20 stress 0.0835775
## ... Procrustes: rmse 1.027368e-05 max resid 4.33024e-05
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09932353
## Run 1 stress 0.0984318
## ... New best solution
## ... Procrustes: rmse 0.0104003 max resid 0.05777218
## Run 2 stress 0.09843014
## ... New best solution
## ... Procrustes: rmse 0.0002115517 max resid 0.0008317289
## ... Similar to previous best
## Run 3 stress 0.09593944
## ... New best solution
## ... Procrustes: rmse 0.03044474 max resid 0.154073
## Run 4 stress 0.09594304
## ... Procrustes: rmse 0.0007449018 max resid 0.004894359
## ... Similar to previous best
## Run 5 stress 0.09594093
## ... Procrustes: rmse 0.000596224 max resid 0.003853818
## ... Similar to previous best
## Run 6 stress 0.09843232
## Run 7 stress 0.09843301
## Run 8 stress 0.09593959
## ... Procrustes: rmse 3.672048e-05 max resid 0.000144838
## ... Similar to previous best
## Run 9 stress 0.09843251
## Run 10 stress 0.0959394
## ... New best solution
## ... Procrustes: rmse 0.0003317936 max resid 0.001965994
## ... Similar to previous best
## Run 11 stress 0.09843166
## Run 12 stress 0.09593932
## ... New best solution
## ... Procrustes: rmse 0.0002921705 max resid 0.001753039
## ... Similar to previous best
## Run 13 stress 0.09932279
## Run 14 stress 0.09843134
## Run 15 stress 0.09843174
## Run 16 stress 0.09594036
## ... Procrustes: rmse 0.0004858126 max resid 0.003135034
## ... Similar to previous best
## Run 17 stress 0.09843023
## Run 18 stress 0.09593958
## ... Procrustes: rmse 0.0003468084 max resid 0.002170641
## ... Similar to previous best
## Run 19 stress 0.09932407
## Run 20 stress 0.09593933
## ... Procrustes: rmse 1.132793e-05 max resid 3.7321e-05
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1066799
## Run 1 stress 0.1076751
## Run 2 stress 0.1076784
## Run 3 stress 0.1076765
## Run 4 stress 0.1057466
## ... New best solution
## ... Procrustes: rmse 0.02311791 max resid 0.1215968
## Run 5 stress 0.1076743
## Run 6 stress 0.1057477
## ... Procrustes: rmse 0.0001968286 max resid 0.0006912121
## ... Similar to previous best
## Run 7 stress 0.1057467
## ... Procrustes: rmse 5.600574e-05 max resid 0.0003069181
## ... Similar to previous best
## Run 8 stress 0.1057461
## ... New best solution
## ... Procrustes: rmse 0.0001077062 max resid 0.0003066837
## ... Similar to previous best
## Run 9 stress 0.1057468
## ... Procrustes: rmse 0.0003543134 max resid 0.001096729
## ... Similar to previous best
## Run 10 stress 0.1057465
## ... Procrustes: rmse 8.409558e-05 max resid 0.0002488517
## ... Similar to previous best
## Run 11 stress 0.1060363
## ... Procrustes: rmse 0.03599433 max resid 0.1347833
## Run 12 stress 0.1060371
## ... Procrustes: rmse 0.03590769 max resid 0.1347016
## Run 13 stress 0.1076763
## Run 14 stress 0.1060351
## ... Procrustes: rmse 0.03620896 max resid 0.1349582
## Run 15 stress 0.1057481
## ... Procrustes: rmse 0.0002856175 max resid 0.000921147
## ... Similar to previous best
## Run 16 stress 0.1057477
## ... Procrustes: rmse 0.0002413474 max resid 0.0007939904
## ... Similar to previous best
## Run 17 stress 0.1057483
## ... Procrustes: rmse 0.0003660193 max resid 0.001261328
## ... Similar to previous best
## Run 18 stress 0.1076766
## Run 19 stress 0.1057466
## ... Procrustes: rmse 0.0003599134 max resid 0.001080599
## ... Similar to previous best
## Run 20 stress 0.1057488
## ... Procrustes: rmse 0.0004035886 max resid 0.001400508
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08190885
## Run 1 stress 0.08212793
## ... Procrustes: rmse 0.006507115 max resid 0.0406766
## Run 2 stress 0.08213592
## ... Procrustes: rmse 0.007034557 max resid 0.04393245
## Run 3 stress 0.08212813
## ... Procrustes: rmse 0.0065163 max resid 0.04073186
## Run 4 stress 0.08443189
## Run 5 stress 0.08443199
## Run 6 stress 0.08212678
## ... Procrustes: rmse 0.006390256 max resid 0.03993689
## Run 7 stress 0.08212031
## ... Procrustes: rmse 0.005956041 max resid 0.0372044
## Run 8 stress 0.08212467
## ... Procrustes: rmse 0.006260704 max resid 0.03912373
## Run 9 stress 0.08190889
## ... Procrustes: rmse 3.582204e-05 max resid 0.0001726637
## ... Similar to previous best
## Run 10 stress 0.08190883
## ... New best solution
## ... Procrustes: rmse 4.713726e-05 max resid 0.0002205685
## ... Similar to previous best
## Run 11 stress 0.08213004
## ... Procrustes: rmse 0.006685334 max resid 0.04183871
## Run 12 stress 0.08212974
## ... Procrustes: rmse 0.006663342 max resid 0.04170315
## Run 13 stress 0.08213359
## ... Procrustes: rmse 0.006937145 max resid 0.04339651
## Run 14 stress 0.08190914
## ... Procrustes: rmse 4.347432e-05 max resid 0.0001620763
## ... Similar to previous best
## Run 15 stress 0.08190989
## ... Procrustes: rmse 0.0002108423 max resid 0.001148117
## ... Similar to previous best
## Run 16 stress 0.08212624
## ... Procrustes: rmse 0.006363967 max resid 0.0398307
## Run 17 stress 0.08190933
## ... Procrustes: rmse 4.560874e-05 max resid 0.0002599741
## ... Similar to previous best
## Run 18 stress 0.08190905
## ... Procrustes: rmse 5.001966e-05 max resid 0.000252484
## ... Similar to previous best
## Run 19 stress 0.08443233
## Run 20 stress 0.0844317
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0961181
## Run 1 stress 0.09611728
## ... New best solution
## ... Procrustes: rmse 0.001534403 max resid 0.006311335
## ... Similar to previous best
## Run 2 stress 0.09611549
## ... New best solution
## ... Procrustes: rmse 0.001216234 max resid 0.004967387
## ... Similar to previous best
## Run 3 stress 0.09611499
## ... New best solution
## ... Procrustes: rmse 0.0009164347 max resid 0.003781783
## ... Similar to previous best
## Run 4 stress 0.09611617
## ... Procrustes: rmse 0.001011884 max resid 0.004204722
## ... Similar to previous best
## Run 5 stress 0.09611717
## ... Procrustes: rmse 0.0002256515 max resid 0.0009568474
## ... Similar to previous best
## Run 6 stress 0.09611551
## ... Procrustes: rmse 7.634253e-05 max resid 0.0003212926
## ... Similar to previous best
## Run 7 stress 0.09611751
## ... Procrustes: rmse 0.001174544 max resid 0.004896106
## ... Similar to previous best
## Run 8 stress 0.0961183
## ... Procrustes: rmse 0.001260562 max resid 0.005267722
## ... Similar to previous best
## Run 9 stress 0.09611496
## ... New best solution
## ... Procrustes: rmse 7.796375e-05 max resid 0.0004770842
## ... Similar to previous best
## Run 10 stress 0.09611428
## ... New best solution
## ... Procrustes: rmse 0.0001604013 max resid 0.0009040269
## ... Similar to previous best
## Run 11 stress 0.0961179
## ... Procrustes: rmse 0.001059152 max resid 0.004456681
## ... Similar to previous best
## Run 12 stress 0.09611527
## ... Procrustes: rmse 0.0002105909 max resid 0.0008668645
## ... Similar to previous best
## Run 13 stress 0.09611797
## ... Procrustes: rmse 0.000534314 max resid 0.002233256
## ... Similar to previous best
## Run 14 stress 0.09611832
## ... Procrustes: rmse 0.001098526 max resid 0.004628895
## ... Similar to previous best
## Run 15 stress 0.0961167
## ... Procrustes: rmse 0.0009199504 max resid 0.003853301
## ... Similar to previous best
## Run 16 stress 0.09611573
## ... Procrustes: rmse 0.0002810339 max resid 0.001281665
## ... Similar to previous best
## Run 17 stress 0.09611734
## ... Procrustes: rmse 0.0004611139 max resid 0.001893511
## ... Similar to previous best
## Run 18 stress 0.09611746
## ... Procrustes: rmse 0.001012763 max resid 0.004259981
## ... Similar to previous best
## Run 19 stress 0.09611485
## ... Procrustes: rmse 0.0001204216 max resid 0.0004839872
## ... Similar to previous best
## Run 20 stress 0.09611546
## ... Procrustes: rmse 0.0007645561 max resid 0.003193129
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1099301
## Run 1 stress 0.1099318
## ... Procrustes: rmse 0.0004140296 max resid 0.001545275
## ... Similar to previous best
## Run 2 stress 0.1179469
## Run 3 stress 0.1099305
## ... Procrustes: rmse 0.0002158247 max resid 0.0007781786
## ... Similar to previous best
## Run 4 stress 0.1099299
## ... New best solution
## ... Procrustes: rmse 8.969293e-05 max resid 0.0004285709
## ... Similar to previous best
## Run 5 stress 0.1099308
## ... Procrustes: rmse 0.0002483831 max resid 0.0009234473
## ... Similar to previous best
## Run 6 stress 0.1099301
## ... Procrustes: rmse 9.425112e-05 max resid 0.0004745901
## ... Similar to previous best
## Run 7 stress 0.1099303
## ... Procrustes: rmse 0.0002736489 max resid 0.001153758
## ... Similar to previous best
## Run 8 stress 0.1099307
## ... Procrustes: rmse 7.847177e-05 max resid 0.0002777343
## ... Similar to previous best
## Run 9 stress 0.109931
## ... Procrustes: rmse 0.0004076753 max resid 0.001760855
## ... Similar to previous best
## Run 10 stress 0.1179496
## Run 11 stress 0.1099305
## ... Procrustes: rmse 0.0001876644 max resid 0.0006926543
## ... Similar to previous best
## Run 12 stress 0.1099308
## ... Procrustes: rmse 0.0003645297 max resid 0.001521797
## ... Similar to previous best
## Run 13 stress 0.1179471
## Run 14 stress 0.10993
## ... Procrustes: rmse 0.000136739 max resid 0.0006121061
## ... Similar to previous best
## Run 15 stress 0.1099303
## ... Procrustes: rmse 0.000257145 max resid 0.001115565
## ... Similar to previous best
## Run 16 stress 0.1099301
## ... Procrustes: rmse 0.0001956494 max resid 0.0008507498
## ... Similar to previous best
## Run 17 stress 0.1099299
## ... New best solution
## ... Procrustes: rmse 3.16826e-05 max resid 0.0001332008
## ... Similar to previous best
## Run 18 stress 0.1099308
## ... Procrustes: rmse 0.0003280453 max resid 0.001400137
## ... Similar to previous best
## Run 19 stress 0.1099305
## ... Procrustes: rmse 0.0002551527 max resid 0.001067019
## ... Similar to previous best
## Run 20 stress 0.1179503
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08381648
## Run 1 stress 0.0832827
## ... New best solution
## ... Procrustes: rmse 0.01423435 max resid 0.1035322
## Run 2 stress 0.08328312
## ... Procrustes: rmse 0.0001023973 max resid 0.0006241897
## ... Similar to previous best
## Run 3 stress 0.0832831
## ... Procrustes: rmse 9.675853e-05 max resid 0.0005890718
## ... Similar to previous best
## Run 4 stress 0.08328377
## ... Procrustes: rmse 0.0001810744 max resid 0.001097136
## ... Similar to previous best
## Run 5 stress 0.08328342
## ... Procrustes: rmse 0.0001243485 max resid 0.0007533637
## ... Similar to previous best
## Run 6 stress 0.08381248
## Run 7 stress 0.08328257
## ... New best solution
## ... Procrustes: rmse 9.449508e-05 max resid 0.0004942327
## ... Similar to previous best
## Run 8 stress 0.08328388
## ... Procrustes: rmse 0.000292619 max resid 0.001702178
## ... Similar to previous best
## Run 9 stress 0.08328361
## ... Procrustes: rmse 0.0002643208 max resid 0.001545761
## ... Similar to previous best
## Run 10 stress 0.08328258
## ... Procrustes: rmse 2.456389e-05 max resid 0.0001168447
## ... Similar to previous best
## Run 11 stress 0.08328319
## ... Procrustes: rmse 0.0001716743 max resid 0.0009780238
## ... Similar to previous best
## Run 12 stress 0.1050654
## Run 13 stress 0.08328325
## ... Procrustes: rmse 0.0002159286 max resid 0.001242848
## ... Similar to previous best
## Run 14 stress 0.08381515
## Run 15 stress 0.0832827
## ... Procrustes: rmse 9.488326e-05 max resid 0.0005452454
## ... Similar to previous best
## Run 16 stress 0.08381612
## Run 17 stress 0.1050621
## Run 18 stress 0.105063
## Run 19 stress 0.0838151
## Run 20 stress 0.083818
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1041644
## Run 1 stress 0.1041625
## ... New best solution
## ... Procrustes: rmse 0.0003037359 max resid 0.001473392
## ... Similar to previous best
## Run 2 stress 0.1040527
## ... New best solution
## ... Procrustes: rmse 0.005984428 max resid 0.03760406
## Run 3 stress 0.1110082
## Run 4 stress 0.1041626
## ... Procrustes: rmse 0.005998679 max resid 0.03767646
## Run 5 stress 0.1040521
## ... New best solution
## ... Procrustes: rmse 9.760811e-05 max resid 0.0004987654
## ... Similar to previous best
## Run 6 stress 0.1033648
## ... New best solution
## ... Procrustes: rmse 0.0119179 max resid 0.08390788
## Run 7 stress 0.1110063
## Run 8 stress 0.1033648
## ... New best solution
## ... Procrustes: rmse 3.915977e-05 max resid 0.0001323147
## ... Similar to previous best
## Run 9 stress 0.1033647
## ... New best solution
## ... Procrustes: rmse 5.16793e-05 max resid 0.0002119283
## ... Similar to previous best
## Run 10 stress 0.1033653
## ... Procrustes: rmse 0.000210657 max resid 0.0008244959
## ... Similar to previous best
## Run 11 stress 0.1110072
## Run 12 stress 0.1116054
## Run 13 stress 0.103365
## ... Procrustes: rmse 0.0001334103 max resid 0.0006515753
## ... Similar to previous best
## Run 14 stress 0.1033648
## ... Procrustes: rmse 5.359865e-05 max resid 0.0002164096
## ... Similar to previous best
## Run 15 stress 0.1033656
## ... Procrustes: rmse 0.0002553542 max resid 0.001060428
## ... Similar to previous best
## Run 16 stress 0.1033657
## ... Procrustes: rmse 0.0002758165 max resid 0.001159428
## ... Similar to previous best
## Run 17 stress 0.1110065
## Run 18 stress 0.1033651
## ... Procrustes: rmse 0.0001752628 max resid 0.0006173408
## ... Similar to previous best
## Run 19 stress 0.1033647
## ... Procrustes: rmse 2.565979e-05 max resid 0.0001128623
## ... Similar to previous best
## Run 20 stress 0.1041625
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08877039
## Run 1 stress 0.08877039
## ... New best solution
## ... Procrustes: rmse 1.230745e-05 max resid 5.641623e-05
## ... Similar to previous best
## Run 2 stress 0.08877042
## ... Procrustes: rmse 3.2707e-05 max resid 0.0001890862
## ... Similar to previous best
## Run 3 stress 0.08877059
## ... Procrustes: rmse 0.000100396 max resid 0.0007076914
## ... Similar to previous best
## Run 4 stress 0.08877042
## ... Procrustes: rmse 2.148744e-05 max resid 6.451256e-05
## ... Similar to previous best
## Run 5 stress 0.08877044
## ... Procrustes: rmse 4.420123e-05 max resid 0.0003131291
## ... Similar to previous best
## Run 6 stress 0.08877042
## ... Procrustes: rmse 1.808169e-05 max resid 6.198966e-05
## ... Similar to previous best
## Run 7 stress 0.08877046
## ... Procrustes: rmse 6.296081e-05 max resid 0.000248557
## ... Similar to previous best
## Run 8 stress 0.08877039
## ... New best solution
## ... Procrustes: rmse 1.136998e-05 max resid 4.613626e-05
## ... Similar to previous best
## Run 9 stress 0.08877039
## ... Procrustes: rmse 5.552613e-06 max resid 3.790367e-05
## ... Similar to previous best
## Run 10 stress 0.08877046
## ... Procrustes: rmse 5.61557e-05 max resid 0.0002991419
## ... Similar to previous best
## Run 11 stress 0.08877041
## ... Procrustes: rmse 1.090928e-05 max resid 4.508346e-05
## ... Similar to previous best
## Run 12 stress 0.08877045
## ... Procrustes: rmse 5.175765e-05 max resid 0.0002103899
## ... Similar to previous best
## Run 13 stress 0.08877052
## ... Procrustes: rmse 9.462948e-05 max resid 0.0006280546
## ... Similar to previous best
## Run 14 stress 0.08877052
## ... Procrustes: rmse 4.700974e-05 max resid 0.0001961339
## ... Similar to previous best
## Run 15 stress 0.0887704
## ... Procrustes: rmse 1.867596e-05 max resid 0.0001225216
## ... Similar to previous best
## Run 16 stress 0.08877043
## ... Procrustes: rmse 1.616716e-05 max resid 7.772941e-05
## ... Similar to previous best
## Run 17 stress 0.08877054
## ... Procrustes: rmse 7.179423e-05 max resid 0.0002712936
## ... Similar to previous best
## Run 18 stress 0.08877052
## ... Procrustes: rmse 6.902306e-05 max resid 0.0003015362
## ... Similar to previous best
## Run 19 stress 0.0887704
## ... Procrustes: rmse 9.809286e-06 max resid 4.207407e-05
## ... Similar to previous best
## Run 20 stress 0.0887704
## ... Procrustes: rmse 2.570502e-05 max resid 0.000139491
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09483809
## Run 1 stress 0.09483761
## ... New best solution
## ... Procrustes: rmse 0.0001572719 max resid 0.001116642
## ... Similar to previous best
## Run 2 stress 0.0948418
## ... Procrustes: rmse 0.001936089 max resid 0.01439276
## Run 3 stress 0.09483831
## ... Procrustes: rmse 0.0001906393 max resid 0.001357448
## ... Similar to previous best
## Run 4 stress 0.09484757
## ... Procrustes: rmse 0.003040681 max resid 0.02265513
## Run 5 stress 0.0948389
## ... Procrustes: rmse 0.0002878993 max resid 0.002066576
## ... Similar to previous best
## Run 6 stress 0.09485579
## ... Procrustes: rmse 0.003854468 max resid 0.02868792
## Run 7 stress 0.09484759
## ... Procrustes: rmse 0.003042327 max resid 0.02266585
## Run 8 stress 0.09483834
## ... Procrustes: rmse 0.000222234 max resid 0.001612226
## ... Similar to previous best
## Run 9 stress 0.09485255
## ... Procrustes: rmse 0.003623672 max resid 0.02696925
## Run 10 stress 0.09485614
## ... Procrustes: rmse 0.003929633 max resid 0.02924022
## Run 11 stress 0.09483878
## ... Procrustes: rmse 0.0002997174 max resid 0.00217378
## ... Similar to previous best
## Run 12 stress 0.09485145
## ... Procrustes: rmse 0.003498991 max resid 0.02606732
## Run 13 stress 0.09485511
## ... Procrustes: rmse 0.003852453 max resid 0.02866975
## Run 14 stress 0.09485159
## ... Procrustes: rmse 0.003527798 max resid 0.02627817
## Run 15 stress 0.09483803
## ... Procrustes: rmse 0.0001578844 max resid 0.001128282
## ... Similar to previous best
## Run 16 stress 0.09485504
## ... Procrustes: rmse 0.003831363 max resid 0.02850523
## Run 17 stress 0.09483899
## ... Procrustes: rmse 0.0003249813 max resid 0.002323756
## ... Similar to previous best
## Run 18 stress 0.0948496
## ... Procrustes: rmse 0.003309988 max resid 0.02466139
## Run 19 stress 0.09485324
## ... Procrustes: rmse 0.003686152 max resid 0.02744993
## Run 20 stress 0.09485154
## ... Procrustes: rmse 0.003435369 max resid 0.02558228
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.06608951
## Run 1 stress 0.06608957
## ... Procrustes: rmse 9.596609e-05 max resid 0.0005644808
## ... Similar to previous best
## Run 2 stress 0.06608992
## ... Procrustes: rmse 0.0001740889 max resid 0.001024336
## ... Similar to previous best
## Run 3 stress 0.0660897
## ... Procrustes: rmse 7.052492e-05 max resid 0.000392195
## ... Similar to previous best
## Run 4 stress 0.06608971
## ... Procrustes: rmse 0.000138014 max resid 0.000864539
## ... Similar to previous best
## Run 5 stress 0.0660896
## ... Procrustes: rmse 3.378383e-05 max resid 0.0002033554
## ... Similar to previous best
## Run 6 stress 0.06608994
## ... Procrustes: rmse 0.0001000638 max resid 0.0005893419
## ... Similar to previous best
## Run 7 stress 0.1061226
## Run 8 stress 0.0660898
## ... Procrustes: rmse 0.0001599026 max resid 0.0009018106
## ... Similar to previous best
## Run 9 stress 0.06608958
## ... Procrustes: rmse 4.509987e-05 max resid 0.0002424317
## ... Similar to previous best
## Run 10 stress 0.06608949
## ... New best solution
## ... Procrustes: rmse 4.458967e-05 max resid 0.0002774656
## ... Similar to previous best
## Run 11 stress 0.0660896
## ... Procrustes: rmse 8.949078e-05 max resid 0.0006007087
## ... Similar to previous best
## Run 12 stress 0.06608979
## ... Procrustes: rmse 0.0001274196 max resid 0.0006068881
## ... Similar to previous best
## Run 13 stress 0.06608949
## ... New best solution
## ... Procrustes: rmse 4.043232e-05 max resid 0.0002488505
## ... Similar to previous best
## Run 14 stress 0.06608947
## ... New best solution
## ... Procrustes: rmse 2.912364e-05 max resid 0.0001880652
## ... Similar to previous best
## Run 15 stress 0.06608952
## ... Procrustes: rmse 2.947219e-05 max resid 0.0001504271
## ... Similar to previous best
## Run 16 stress 0.06608984
## ... Procrustes: rmse 0.0001284738 max resid 0.0007676231
## ... Similar to previous best
## Run 17 stress 0.06608958
## ... Procrustes: rmse 7.510331e-05 max resid 0.0004653102
## ... Similar to previous best
## Run 18 stress 0.06608985
## ... Procrustes: rmse 0.0001326414 max resid 0.0008258256
## ... Similar to previous best
## Run 19 stress 0.06608972
## ... Procrustes: rmse 9.642526e-05 max resid 0.000540934
## ... Similar to previous best
## Run 20 stress 0.06608947
## ... Procrustes: rmse 1.686598e-05 max resid 8.829058e-05
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1022632
## Run 1 stress 0.1022629
## ... New best solution
## ... Procrustes: rmse 8.31549e-05 max resid 0.0002492188
## ... Similar to previous best
## Run 2 stress 0.1035119
## Run 3 stress 0.1035086
## Run 4 stress 0.1035093
## Run 5 stress 0.1022631
## ... Procrustes: rmse 0.0001527899 max resid 0.0005272731
## ... Similar to previous best
## Run 6 stress 0.1022629
## ... New best solution
## ... Procrustes: rmse 5.691167e-05 max resid 0.0002076609
## ... Similar to previous best
## Run 7 stress 0.1112375
## Run 8 stress 0.102263
## ... Procrustes: rmse 5.354298e-05 max resid 0.0001524059
## ... Similar to previous best
## Run 9 stress 0.1035077
## Run 10 stress 0.1112288
## Run 11 stress 0.1022629
## ... Procrustes: rmse 7.506715e-05 max resid 0.0002269579
## ... Similar to previous best
## Run 12 stress 0.1035096
## Run 13 stress 0.102263
## ... Procrustes: rmse 3.58014e-05 max resid 0.0001326026
## ... Similar to previous best
## Run 14 stress 0.111231
## Run 15 stress 0.1112322
## Run 16 stress 0.1112338
## Run 17 stress 0.1035105
## Run 18 stress 0.1112361
## Run 19 stress 0.1035095
## Run 20 stress 0.1022631
## ... Procrustes: rmse 0.0001024037 max resid 0.0003217259
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09680038
## Run 1 stress 0.09680006
## ... New best solution
## ... Procrustes: rmse 0.0002017815 max resid 0.0006003235
## ... Similar to previous best
## Run 2 stress 0.1121599
## Run 3 stress 0.09680171
## ... Procrustes: rmse 0.0003363481 max resid 0.001350219
## ... Similar to previous best
## Run 4 stress 0.0968
## ... New best solution
## ... Procrustes: rmse 8.15947e-05 max resid 0.0003518625
## ... Similar to previous best
## Run 5 stress 0.1088881
## Run 6 stress 0.09680068
## ... Procrustes: rmse 0.0002323681 max resid 0.0008498104
## ... Similar to previous best
## Run 7 stress 0.1121655
## Run 8 stress 0.1089042
## Run 9 stress 0.09680024
## ... Procrustes: rmse 7.398517e-05 max resid 0.0002687824
## ... Similar to previous best
## Run 10 stress 0.09680012
## ... Procrustes: rmse 9.488498e-05 max resid 0.0004097133
## ... Similar to previous best
## Run 11 stress 0.1088904
## Run 12 stress 0.108897
## Run 13 stress 0.09680033
## ... Procrustes: rmse 0.0001610846 max resid 0.0006253535
## ... Similar to previous best
## Run 14 stress 0.0968001
## ... Procrustes: rmse 7.130016e-05 max resid 0.0003289378
## ... Similar to previous best
## Run 15 stress 0.1088777
## Run 16 stress 0.1088786
## Run 17 stress 0.09680024
## ... Procrustes: rmse 0.0001288292 max resid 0.0005002904
## ... Similar to previous best
## Run 18 stress 0.09680002
## ... Procrustes: rmse 4.454797e-05 max resid 0.0002306613
## ... Similar to previous best
## Run 19 stress 0.09680015
## ... Procrustes: rmse 4.966749e-05 max resid 0.0001792979
## ... Similar to previous best
## Run 20 stress 0.09680173
## ... Procrustes: rmse 0.0003957039 max resid 0.001412882
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08730166
## Run 1 stress 0.08730202
## ... Procrustes: rmse 0.00015845 max resid 0.001137418
## ... Similar to previous best
## Run 2 stress 0.08730244
## ... Procrustes: rmse 0.0002464015 max resid 0.001751035
## ... Similar to previous best
## Run 3 stress 0.08730184
## ... Procrustes: rmse 0.0001105158 max resid 0.0007682411
## ... Similar to previous best
## Run 4 stress 0.08730393
## ... Procrustes: rmse 0.0004302714 max resid 0.003068614
## ... Similar to previous best
## Run 5 stress 0.08730273
## ... Procrustes: rmse 0.00028572 max resid 0.002029081
## ... Similar to previous best
## Run 6 stress 0.08730239
## ... Procrustes: rmse 0.0002405943 max resid 0.001706494
## ... Similar to previous best
## Run 7 stress 0.08730233
## ... Procrustes: rmse 0.0002418445 max resid 0.001718731
## ... Similar to previous best
## Run 8 stress 0.08730177
## ... Procrustes: rmse 0.000101323 max resid 0.0007062679
## ... Similar to previous best
## Run 9 stress 0.08730235
## ... Procrustes: rmse 0.0002378418 max resid 0.001680774
## ... Similar to previous best
## Run 10 stress 0.08730228
## ... Procrustes: rmse 0.0002269513 max resid 0.00167239
## ... Similar to previous best
## Run 11 stress 0.08730219
## ... Procrustes: rmse 0.0002024418 max resid 0.001431484
## ... Similar to previous best
## Run 12 stress 0.08730308
## ... Procrustes: rmse 0.0003370074 max resid 0.002398735
## ... Similar to previous best
## Run 13 stress 0.08730177
## ... Procrustes: rmse 8.915136e-05 max resid 0.0006496489
## ... Similar to previous best
## Run 14 stress 0.0873017
## ... Procrustes: rmse 7.87148e-05 max resid 0.0005676797
## ... Similar to previous best
## Run 15 stress 0.08730205
## ... Procrustes: rmse 0.0001935584 max resid 0.001384629
## ... Similar to previous best
## Run 16 stress 0.08730285
## ... Procrustes: rmse 0.000299159 max resid 0.002125932
## ... Similar to previous best
## Run 17 stress 0.08730193
## ... Procrustes: rmse 0.0001606386 max resid 0.001148359
## ... Similar to previous best
## Run 18 stress 0.08730177
## ... Procrustes: rmse 8.037786e-05 max resid 0.0005486387
## ... Similar to previous best
## Run 19 stress 0.08730207
## ... Procrustes: rmse 0.0001395937 max resid 0.0009668676
## ... Similar to previous best
## Run 20 stress 0.08730178
## ... Procrustes: rmse 0.0001151785 max resid 0.0008303049
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.07255714
## Run 1 stress 0.07255712
## ... New best solution
## ... Procrustes: rmse 0.0001156653 max resid 0.000764618
## ... Similar to previous best
## Run 2 stress 0.07255706
## ... New best solution
## ... Procrustes: rmse 5.117448e-05 max resid 0.0002878759
## ... Similar to previous best
## Run 3 stress 0.07255729
## ... Procrustes: rmse 3.255862e-05 max resid 0.0001367247
## ... Similar to previous best
## Run 4 stress 0.07255718
## ... Procrustes: rmse 8.483079e-05 max resid 0.0005978277
## ... Similar to previous best
## Run 5 stress 0.07255723
## ... Procrustes: rmse 5.717411e-05 max resid 0.0003026472
## ... Similar to previous best
## Run 6 stress 0.0725571
## ... Procrustes: rmse 4.578515e-05 max resid 0.0002814029
## ... Similar to previous best
## Run 7 stress 0.07255743
## ... Procrustes: rmse 0.0001432145 max resid 0.001009616
## ... Similar to previous best
## Run 8 stress 0.07255771
## ... Procrustes: rmse 0.0001664887 max resid 0.001141647
## ... Similar to previous best
## Run 9 stress 0.07255706
## ... Procrustes: rmse 1.558697e-05 max resid 0.0001024634
## ... Similar to previous best
## Run 10 stress 0.07255706
## ... Procrustes: rmse 1.169382e-05 max resid 6.922872e-05
## ... Similar to previous best
## Run 11 stress 0.07255721
## ... Procrustes: rmse 9.294131e-05 max resid 0.0006560508
## ... Similar to previous best
## Run 12 stress 0.07255754
## ... Procrustes: rmse 0.0001609833 max resid 0.001113794
## ... Similar to previous best
## Run 13 stress 0.07255712
## ... Procrustes: rmse 5.113539e-05 max resid 0.0003508757
## ... Similar to previous best
## Run 14 stress 0.07255728
## ... Procrustes: rmse 9.099091e-05 max resid 0.0006319323
## ... Similar to previous best
## Run 15 stress 0.07255706
## ... New best solution
## ... Procrustes: rmse 5.078291e-06 max resid 2.875217e-05
## ... Similar to previous best
## Run 16 stress 0.07255729
## ... Procrustes: rmse 0.0001092795 max resid 0.0007526414
## ... Similar to previous best
## Run 17 stress 0.07255736
## ... Procrustes: rmse 5.670468e-05 max resid 0.000339332
## ... Similar to previous best
## Run 18 stress 0.07255706
## ... Procrustes: rmse 1.615472e-05 max resid 0.0001118949
## ... Similar to previous best
## Run 19 stress 0.07255741
## ... Procrustes: rmse 0.0001318341 max resid 0.0008818734
## ... Similar to previous best
## Run 20 stress 0.07255794
## ... Procrustes: rmse 0.0002148936 max resid 0.001486881
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08716137
## Run 1 stress 0.08716138
## ... Procrustes: rmse 2.153707e-05 max resid 7.617432e-05
## ... Similar to previous best
## Run 2 stress 0.08716137
## ... Procrustes: rmse 1.493027e-05 max resid 5.284686e-05
## ... Similar to previous best
## Run 3 stress 0.08716137
## ... Procrustes: rmse 4.371118e-06 max resid 1.675641e-05
## ... Similar to previous best
## Run 4 stress 0.08716165
## ... Procrustes: rmse 5.617175e-05 max resid 0.0001771544
## ... Similar to previous best
## Run 5 stress 0.08716138
## ... Procrustes: rmse 2.416576e-05 max resid 8.377178e-05
## ... Similar to previous best
## Run 6 stress 0.08716137
## ... Procrustes: rmse 1.679799e-05 max resid 5.760035e-05
## ... Similar to previous best
## Run 7 stress 0.08716141
## ... Procrustes: rmse 3.656023e-05 max resid 0.0001248472
## ... Similar to previous best
## Run 8 stress 0.08716142
## ... Procrustes: rmse 2.851164e-05 max resid 9.182603e-05
## ... Similar to previous best
## Run 9 stress 0.08716137
## ... Procrustes: rmse 1.387596e-05 max resid 4.657057e-05
## ... Similar to previous best
## Run 10 stress 0.08716137
## ... Procrustes: rmse 1.858916e-05 max resid 6.341768e-05
## ... Similar to previous best
## Run 11 stress 0.08716137
## ... Procrustes: rmse 1.49355e-05 max resid 5.166098e-05
## ... Similar to previous best
## Run 12 stress 0.08716139
## ... Procrustes: rmse 1.081488e-05 max resid 4.263305e-05
## ... Similar to previous best
## Run 13 stress 0.08716149
## ... Procrustes: rmse 7.280441e-05 max resid 0.0002583244
## ... Similar to previous best
## Run 14 stress 0.08716165
## ... Procrustes: rmse 0.0001159866 max resid 0.0004038964
## ... Similar to previous best
## Run 15 stress 0.08716139
## ... Procrustes: rmse 3.597778e-05 max resid 0.0001349093
## ... Similar to previous best
## Run 16 stress 0.08716137
## ... Procrustes: rmse 1.873751e-05 max resid 6.73391e-05
## ... Similar to previous best
## Run 17 stress 0.08716141
## ... Procrustes: rmse 4.022367e-05 max resid 0.0001649956
## ... Similar to previous best
## Run 18 stress 0.08716143
## ... Procrustes: rmse 5.199414e-05 max resid 0.0001816184
## ... Similar to previous best
## Run 19 stress 0.08716141
## ... Procrustes: rmse 4.055753e-05 max resid 0.0001413679
## ... Similar to previous best
## Run 20 stress 0.08716149
## ... Procrustes: rmse 7.495187e-05 max resid 0.0002613564
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09356841
## Run 1 stress 0.09357035
## ... Procrustes: rmse 0.001036984 max resid 0.005211025
## ... Similar to previous best
## Run 2 stress 0.09357333
## ... Procrustes: rmse 0.0008103008 max resid 0.004695749
## ... Similar to previous best
## Run 3 stress 0.09692557
## Run 4 stress 0.09358254
## ... Procrustes: rmse 0.001844986 max resid 0.01021623
## Run 5 stress 0.09356815
## ... New best solution
## ... Procrustes: rmse 0.0007470659 max resid 0.004442455
## ... Similar to previous best
## Run 6 stress 0.09692556
## Run 7 stress 0.09357082
## ... Procrustes: rmse 0.0004085872 max resid 0.001922991
## ... Similar to previous best
## Run 8 stress 0.09357083
## ... Procrustes: rmse 0.0004094045 max resid 0.001941384
## ... Similar to previous best
## Run 9 stress 0.09357075
## ... Procrustes: rmse 0.0004009746 max resid 0.001885179
## ... Similar to previous best
## Run 10 stress 0.09356852
## ... Procrustes: rmse 9.689436e-05 max resid 0.000467852
## ... Similar to previous best
## Run 11 stress 0.09357648
## ... Procrustes: rmse 0.002034744 max resid 0.01237333
## Run 12 stress 0.09358526
## ... Procrustes: rmse 0.002638566 max resid 0.01478808
## Run 13 stress 0.09357637
## ... Procrustes: rmse 0.001965432 max resid 0.01307796
## Run 14 stress 0.09692659
## Run 15 stress 0.0969257
## Run 16 stress 0.09357634
## ... Procrustes: rmse 0.002050736 max resid 0.01265703
## Run 17 stress 0.09692764
## Run 18 stress 0.0969287
## Run 19 stress 0.0969254
## Run 20 stress 0.09357036
## ... Procrustes: rmse 0.0003578216 max resid 0.001675408
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.07425622
## Run 1 stress 0.07425669
## ... Procrustes: rmse 0.0001060022 max resid 0.0004985191
## ... Similar to previous best
## Run 2 stress 0.07425746
## ... Procrustes: rmse 0.0002086398 max resid 0.0009986625
## ... Similar to previous best
## Run 3 stress 0.07425618
## ... New best solution
## ... Procrustes: rmse 7.67794e-05 max resid 0.0003454964
## ... Similar to previous best
## Run 4 stress 0.0742561
## ... New best solution
## ... Procrustes: rmse 2.256013e-05 max resid 0.0001352918
## ... Similar to previous best
## Run 5 stress 0.07425608
## ... New best solution
## ... Procrustes: rmse 4.842773e-05 max resid 0.0002051218
## ... Similar to previous best
## Run 6 stress 0.07425637
## ... Procrustes: rmse 0.0001241232 max resid 0.000560555
## ... Similar to previous best
## Run 7 stress 0.07425606
## ... New best solution
## ... Procrustes: rmse 9.780353e-06 max resid 3.804323e-05
## ... Similar to previous best
## Run 8 stress 0.07425719
## ... Procrustes: rmse 0.0002823296 max resid 0.001312254
## ... Similar to previous best
## Run 9 stress 0.07425606
## ... Procrustes: rmse 2.250999e-05 max resid 9.548458e-05
## ... Similar to previous best
## Run 10 stress 0.07425611
## ... Procrustes: rmse 3.350103e-05 max resid 0.0001549904
## ... Similar to previous best
## Run 11 stress 0.07425621
## ... Procrustes: rmse 8.046465e-05 max resid 0.0003712428
## ... Similar to previous best
## Run 12 stress 0.07425614
## ... Procrustes: rmse 8.352501e-05 max resid 0.0003660528
## ... Similar to previous best
## Run 13 stress 0.07425699
## ... Procrustes: rmse 0.0002514561 max resid 0.001164952
## ... Similar to previous best
## Run 14 stress 0.07425676
## ... Procrustes: rmse 0.0002229114 max resid 0.001029828
## ... Similar to previous best
## Run 15 stress 0.07425673
## ... Procrustes: rmse 0.0001729766 max resid 0.000773296
## ... Similar to previous best
## Run 16 stress 0.07425773
## ... Procrustes: rmse 0.000326543 max resid 0.001517172
## ... Similar to previous best
## Run 17 stress 0.07425704
## ... Procrustes: rmse 0.0002523273 max resid 0.001169519
## ... Similar to previous best
## Run 18 stress 0.07425611
## ... Procrustes: rmse 4.175534e-05 max resid 0.0001955961
## ... Similar to previous best
## Run 19 stress 0.07425659
## ... Procrustes: rmse 0.0001607866 max resid 0.0007233893
## ... Similar to previous best
## Run 20 stress 0.07425679
## ... Procrustes: rmse 0.0002004777 max resid 0.0008967147
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09457686
## Run 1 stress 0.09457652
## ... New best solution
## ... Procrustes: rmse 8.56382e-05 max resid 0.0005394522
## ... Similar to previous best
## Run 2 stress 0.09457768
## ... Procrustes: rmse 0.0002082935 max resid 0.001134599
## ... Similar to previous best
## Run 3 stress 0.09457697
## ... Procrustes: rmse 0.0003747623 max resid 0.001981177
## ... Similar to previous best
## Run 4 stress 0.09457786
## ... Procrustes: rmse 0.0002263038 max resid 0.001323804
## ... Similar to previous best
## Run 5 stress 0.09457709
## ... Procrustes: rmse 0.0001051722 max resid 0.0006157543
## ... Similar to previous best
## Run 6 stress 0.09457785
## ... Procrustes: rmse 0.0004744894 max resid 0.002482588
## ... Similar to previous best
## Run 7 stress 0.09457772
## ... Procrustes: rmse 0.0004886311 max resid 0.00254212
## ... Similar to previous best
## Run 8 stress 0.09457756
## ... Procrustes: rmse 0.0004511969 max resid 0.002344732
## ... Similar to previous best
## Run 9 stress 0.09457691
## ... Procrustes: rmse 0.0003694528 max resid 0.001950577
## ... Similar to previous best
## Run 10 stress 0.09457631
## ... New best solution
## ... Procrustes: rmse 0.000113848 max resid 0.0006225658
## ... Similar to previous best
## Run 11 stress 0.09457632
## ... Procrustes: rmse 7.200607e-05 max resid 0.0004055652
## ... Similar to previous best
## Run 12 stress 0.09457704
## ... Procrustes: rmse 0.0002789725 max resid 0.001457425
## ... Similar to previous best
## Run 13 stress 0.09457663
## ... Procrustes: rmse 0.0001914735 max resid 0.001034559
## ... Similar to previous best
## Run 14 stress 0.09457638
## ... Procrustes: rmse 5.882156e-05 max resid 0.0002598129
## ... Similar to previous best
## Run 15 stress 0.09457765
## ... Procrustes: rmse 0.0003182443 max resid 0.001821409
## ... Similar to previous best
## Run 16 stress 0.09457788
## ... Procrustes: rmse 0.0003857223 max resid 0.001986772
## ... Similar to previous best
## Run 17 stress 0.0945771
## ... Procrustes: rmse 0.0002385721 max resid 0.001361465
## ... Similar to previous best
## Run 18 stress 0.09457673
## ... Procrustes: rmse 0.0001567104 max resid 0.0008897796
## ... Similar to previous best
## Run 19 stress 0.09457786
## ... Procrustes: rmse 0.0003421881 max resid 0.001960654
## ... Similar to previous best
## Run 20 stress 0.09457684
## ... Procrustes: rmse 0.0001888611 max resid 0.0010778
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.03145116
## Run 1 stress 0.03145131
## ... Procrustes: rmse 3.279728e-05 max resid 0.0001160832
## ... Similar to previous best
## Run 2 stress 0.03474676
## Run 3 stress 0.04815295
## Run 4 stress 0.05138253
## Run 5 stress 0.03474623
## Run 6 stress 0.03474749
## Run 7 stress 0.05082791
## Run 8 stress 0.03147542
## ... Procrustes: rmse 0.002119487 max resid 0.01096477
## Run 9 stress 0.03474655
## Run 10 stress 0.03145286
## ... Procrustes: rmse 0.001187134 max resid 0.006103472
## ... Similar to previous best
## Run 11 stress 0.03308486
## Run 12 stress 0.03144917
## ... New best solution
## ... Procrustes: rmse 0.000222058 max resid 0.001091374
## ... Similar to previous best
## Run 13 stress 0.03240349
## Run 14 stress 0.03474685
## Run 15 stress 0.03144975
## ... Procrustes: rmse 0.0006273487 max resid 0.003125827
## ... Similar to previous best
## Run 16 stress 0.03144998
## ... Procrustes: rmse 0.0007184706 max resid 0.00377674
## ... Similar to previous best
## Run 17 stress 0.0324039
## Run 18 stress 0.03145163
## ... Procrustes: rmse 0.0008747037 max resid 0.004542233
## ... Similar to previous best
## Run 19 stress 0.03240341
## Run 20 stress 0.03474719
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.632009e-05
## ... Procrustes: rmse 0.0001699321 max resid 0.0007992366
## ... Similar to previous best
## Run 2 stress 9.260983e-05
## ... Procrustes: rmse 0.0001645643 max resid 0.0005972188
## ... Similar to previous best
## Run 3 stress 9.965867e-05
## ... Procrustes: rmse 0.0001675049 max resid 0.0007201619
## ... Similar to previous best
## Run 4 stress 8.114108e-05
## ... Procrustes: rmse 0.0001559394 max resid 0.0007278782
## ... Similar to previous best
## Run 5 stress 9.155602e-05
## ... Procrustes: rmse 0.0001605972 max resid 0.0008314485
## ... Similar to previous best
## Run 6 stress 9.465339e-05
## ... Procrustes: rmse 0.0001618903 max resid 0.0007822471
## ... Similar to previous best
## Run 7 stress 7.221162e-05
## ... Procrustes: rmse 0.0001343336 max resid 0.000593774
## ... Similar to previous best
## Run 8 stress 9.971324e-05
## ... Procrustes: rmse 0.0001660645 max resid 0.0008686937
## ... Similar to previous best
## Run 9 stress 9.594096e-05
## ... Procrustes: rmse 0.0001709714 max resid 0.0009947761
## ... Similar to previous best
## Run 10 stress 9.191044e-05
## ... Procrustes: rmse 0.0001642345 max resid 0.001007921
## ... Similar to previous best
## Run 11 stress 9.265873e-05
## ... Procrustes: rmse 0.0001579337 max resid 0.0006942206
## ... Similar to previous best
## Run 12 stress 9.89023e-05
## ... Procrustes: rmse 0.0001733005 max resid 0.0009301558
## ... Similar to previous best
## Run 13 stress 8.934795e-05
## ... Procrustes: rmse 0.0001688647 max resid 0.0007043231
## ... Similar to previous best
## Run 14 stress 9.694868e-05
## ... Procrustes: rmse 0.0001613317 max resid 0.000621031
## ... Similar to previous best
## Run 15 stress 8.108469e-05
## ... Procrustes: rmse 0.0001530404 max resid 0.0008336713
## ... Similar to previous best
## Run 16 stress 7.745025e-05
## ... Procrustes: rmse 0.0001475472 max resid 0.0006755637
## ... Similar to previous best
## Run 17 stress 9.909513e-05
## ... Procrustes: rmse 0.0001723312 max resid 0.0008152828
## ... Similar to previous best
## Run 18 stress 9.713091e-05
## ... Procrustes: rmse 0.0001267474 max resid 0.0007091027
## ... Similar to previous best
## Run 19 stress 7.785069e-05
## ... Procrustes: rmse 0.000138654 max resid 0.0006463437
## ... Similar to previous best
## Run 20 stress 9.473477e-05
## ... Procrustes: rmse 0.0001637393 max resid 0.000664788
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.782656e-05
## ... Procrustes: rmse 0.0001600914 max resid 0.0009088318
## ... Similar to previous best
## Run 2 stress 9.076693e-05
## ... Procrustes: rmse 0.0001445025 max resid 0.0004463379
## ... Similar to previous best
## Run 3 stress 9.647686e-05
## ... Procrustes: rmse 0.0001657638 max resid 0.0006910255
## ... Similar to previous best
## Run 4 stress 9.793439e-05
## ... Procrustes: rmse 0.000169358 max resid 0.0009356711
## ... Similar to previous best
## Run 5 stress 9.501145e-05
## ... Procrustes: rmse 0.0001727955 max resid 0.0009861154
## ... Similar to previous best
## Run 6 stress 9.161757e-05
## ... Procrustes: rmse 0.0001434626 max resid 0.0004841362
## ... Similar to previous best
## Run 7 stress 8.806723e-05
## ... Procrustes: rmse 0.0001558155 max resid 0.0008586629
## ... Similar to previous best
## Run 8 stress 9.834742e-05
## ... Procrustes: rmse 0.0001668768 max resid 0.0005307136
## ... Similar to previous best
## Run 9 stress 8.418926e-05
## ... Procrustes: rmse 0.0001607761 max resid 0.0008779899
## ... Similar to previous best
## Run 10 stress 9.477751e-05
## ... Procrustes: rmse 0.000155469 max resid 0.000623608
## ... Similar to previous best
## Run 11 stress 9.687941e-05
## ... Procrustes: rmse 0.0001643022 max resid 0.0008180518
## ... Similar to previous best
## Run 12 stress 9.377217e-05
## ... Procrustes: rmse 0.0001669683 max resid 0.000816116
## ... Similar to previous best
## Run 13 stress 9.358112e-05
## ... Procrustes: rmse 0.0001700118 max resid 0.00106679
## ... Similar to previous best
## Run 14 stress 9.436939e-05
## ... Procrustes: rmse 0.0001583334 max resid 0.0004494837
## ... Similar to previous best
## Run 15 stress 8.350099e-05
## ... Procrustes: rmse 0.0001386785 max resid 0.0005663992
## ... Similar to previous best
## Run 16 stress 9.98428e-05
## ... Procrustes: rmse 0.0001689704 max resid 0.0009424901
## ... Similar to previous best
## Run 17 stress 9.222838e-05
## ... Procrustes: rmse 0.0001442069 max resid 0.0005546836
## ... Similar to previous best
## Run 18 stress 8.963101e-05
## ... Procrustes: rmse 0.0001636602 max resid 0.0008327575
## ... Similar to previous best
## Run 19 stress 9.266124e-05
## ... Procrustes: rmse 0.0001526461 max resid 0.0006198067
## ... Similar to previous best
## Run 20 stress 8.948156e-05
## ... Procrustes: rmse 0.0001618322 max resid 0.0006446196
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.389511e-05
## ... Procrustes: rmse 0.0001710008 max resid 0.0009714308
## ... Similar to previous best
## Run 2 stress 9.494326e-05
## ... Procrustes: rmse 0.0001806372 max resid 0.0007274808
## ... Similar to previous best
## Run 3 stress 9.396603e-05
## ... Procrustes: rmse 0.0001659193 max resid 0.0008346312
## ... Similar to previous best
## Run 4 stress 9.376319e-05
## ... Procrustes: rmse 0.0001562745 max resid 0.0006161703
## ... Similar to previous best
## Run 5 stress 9.824013e-05
## ... Procrustes: rmse 0.0001662413 max resid 0.0008024195
## ... Similar to previous best
## Run 6 stress 8.969292e-05
## ... Procrustes: rmse 0.0001672052 max resid 0.0006796589
## ... Similar to previous best
## Run 7 stress 9.729724e-05
## ... Procrustes: rmse 0.0001757725 max resid 0.001013696
## ... Similar to previous best
## Run 8 stress 9.830966e-05
## ... Procrustes: rmse 0.0001692138 max resid 0.001062224
## ... Similar to previous best
## Run 9 stress 7.712417e-05
## ... Procrustes: rmse 0.0001118452 max resid 0.0006231916
## ... Similar to previous best
## Run 10 stress 8.777176e-05
## ... Procrustes: rmse 0.0001487423 max resid 0.0006648963
## ... Similar to previous best
## Run 11 stress 9.379748e-05
## ... Procrustes: rmse 0.0001641003 max resid 0.0009175692
## ... Similar to previous best
## Run 12 stress 9.619192e-05
## ... Procrustes: rmse 0.0001792569 max resid 0.0008104087
## ... Similar to previous best
## Run 13 stress 9.758359e-05
## ... Procrustes: rmse 0.0001847043 max resid 0.0009897865
## ... Similar to previous best
## Run 14 stress 9.785982e-05
## ... Procrustes: rmse 0.0001784962 max resid 0.0007752715
## ... Similar to previous best
## Run 15 stress 9.24782e-05
## ... Procrustes: rmse 0.0001675024 max resid 0.0008643654
## ... Similar to previous best
## Run 16 stress 9.219828e-05
## ... Procrustes: rmse 0.0001779424 max resid 0.001065759
## ... Similar to previous best
## Run 17 stress 9.287813e-05
## ... Procrustes: rmse 0.000176535 max resid 0.000855474
## ... Similar to previous best
## Run 18 stress 9.631619e-05
## ... Procrustes: rmse 0.0001779272 max resid 0.0009054911
## ... Similar to previous best
## Run 19 stress 8.254114e-05
## ... Procrustes: rmse 0.0001600632 max resid 0.0008835198
## ... Similar to previous best
## Run 20 stress 9.517273e-05
## ... Procrustes: rmse 0.0001701944 max resid 0.001058368
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.967443e-05
## ... Procrustes: rmse 0.0001871324 max resid 0.0008559439
## ... Similar to previous best
## Run 2 stress 9.166455e-05
## ... Procrustes: rmse 0.0001542267 max resid 0.0006387039
## ... Similar to previous best
## Run 3 stress 9.476745e-05
## ... Procrustes: rmse 0.0001778307 max resid 0.0007284299
## ... Similar to previous best
## Run 4 stress 9.644968e-05
## ... Procrustes: rmse 0.0001866326 max resid 0.0009043548
## ... Similar to previous best
## Run 5 stress 9.366326e-05
## ... Procrustes: rmse 0.0001684369 max resid 0.0009041758
## ... Similar to previous best
## Run 6 stress 9.621914e-05
## ... Procrustes: rmse 0.0001800118 max resid 0.0008702901
## ... Similar to previous best
## Run 7 stress 9.688422e-05
## ... Procrustes: rmse 0.0001709049 max resid 0.0007156161
## ... Similar to previous best
## Run 8 stress 9.811745e-05
## ... Procrustes: rmse 0.000175149 max resid 0.0008234501
## ... Similar to previous best
## Run 9 stress 9.316075e-05
## ... Procrustes: rmse 0.0001788217 max resid 0.0008116632
## ... Similar to previous best
## Run 10 stress 9.445255e-05
## ... Procrustes: rmse 0.0001900643 max resid 0.0008028325
## ... Similar to previous best
## Run 11 stress 9.691711e-05
## ... Procrustes: rmse 0.0001814941 max resid 0.0008033564
## ... Similar to previous best
## Run 12 stress 9.94416e-05
## ... Procrustes: rmse 0.0001821059 max resid 0.0008938197
## ... Similar to previous best
## Run 13 stress 9.443519e-05
## ... Procrustes: rmse 0.0001791872 max resid 0.0007701855
## ... Similar to previous best
## Run 14 stress 9.227803e-05
## ... Procrustes: rmse 0.0001833004 max resid 0.000655691
## ... Similar to previous best
## Run 15 stress 9.066071e-05
## ... Procrustes: rmse 0.0001736596 max resid 0.0008529364
## ... Similar to previous best
## Run 16 stress 9.968522e-05
## ... Procrustes: rmse 0.0001797289 max resid 0.0006679259
## ... Similar to previous best
## Run 17 stress 8.890572e-05
## ... Procrustes: rmse 0.0001560661 max resid 0.0006960994
## ... Similar to previous best
## Run 18 stress 9.422499e-05
## ... Procrustes: rmse 0.00017043 max resid 0.0007555549
## ... Similar to previous best
## Run 19 stress 9.998956e-05
## ... Procrustes: rmse 0.0001792095 max resid 0.0009375417
## ... Similar to previous best
## Run 20 stress 9.97905e-05
## ... Procrustes: rmse 0.0001885226 max resid 0.0007653317
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.712037e-05
## ... Procrustes: rmse 0.0002107925 max resid 0.0009715774
## ... Similar to previous best
## Run 2 stress 9.412747e-05
## ... Procrustes: rmse 0.0001926185 max resid 0.001109457
## ... Similar to previous best
## Run 3 stress 9.544353e-05
## ... Procrustes: rmse 0.0002138345 max resid 0.001405294
## ... Similar to previous best
## Run 4 stress 9.894342e-05
## ... Procrustes: rmse 0.0002107077 max resid 0.00116083
## ... Similar to previous best
## Run 5 stress 9.401533e-05
## ... Procrustes: rmse 0.0001764736 max resid 0.0005563946
## ... Similar to previous best
## Run 6 stress 9.408201e-05
## ... Procrustes: rmse 0.0002179988 max resid 0.001201521
## ... Similar to previous best
## Run 7 stress 8.582163e-05
## ... Procrustes: rmse 0.0001850467 max resid 0.001096918
## ... Similar to previous best
## Run 8 stress 9.804761e-05
## ... Procrustes: rmse 0.0002087738 max resid 0.0008784205
## ... Similar to previous best
## Run 9 stress 9.136583e-05
## ... Procrustes: rmse 0.0002183181 max resid 0.001042261
## ... Similar to previous best
## Run 10 stress 8.087634e-05
## ... Procrustes: rmse 0.0001963005 max resid 0.001276537
## ... Similar to previous best
## Run 11 stress 9.955872e-05
## ... Procrustes: rmse 0.0001626829 max resid 0.0007910741
## ... Similar to previous best
## Run 12 stress 9.746458e-05
## ... Procrustes: rmse 0.0002138063 max resid 0.001415276
## ... Similar to previous best
## Run 13 stress 9.529235e-05
## ... Procrustes: rmse 0.0002152088 max resid 0.0009392457
## ... Similar to previous best
## Run 14 stress 9.740543e-05
## ... Procrustes: rmse 0.0001790374 max resid 0.0008629879
## ... Similar to previous best
## Run 15 stress 9.266411e-05
## ... Procrustes: rmse 0.0001935416 max resid 0.0007210835
## ... Similar to previous best
## Run 16 stress 9.396621e-05
## ... Procrustes: rmse 0.0001899526 max resid 0.0007799619
## ... Similar to previous best
## Run 17 stress 9.998812e-05
## ... Procrustes: rmse 0.0002287227 max resid 0.0009322135
## ... Similar to previous best
## Run 18 stress 9.318003e-05
## ... Procrustes: rmse 0.0002038071 max resid 0.0009629113
## ... Similar to previous best
## Run 19 stress 9.64176e-05
## ... Procrustes: rmse 0.0001981528 max resid 0.001037485
## ... Similar to previous best
## Run 20 stress 9.192169e-05
## ... Procrustes: rmse 0.0001912103 max resid 0.0007596146
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.179001e-05
## ... Procrustes: rmse 0.0001715578 max resid 0.000656364
## ... Similar to previous best
## Run 2 stress 9.168266e-05
## ... Procrustes: rmse 0.000186514 max resid 0.001138935
## ... Similar to previous best
## Run 3 stress 9.468798e-05
## ... Procrustes: rmse 0.0001887245 max resid 0.00120904
## ... Similar to previous best
## Run 4 stress 8.782093e-05
## ... Procrustes: rmse 0.0001513998 max resid 0.0006658898
## ... Similar to previous best
## Run 5 stress 9.169685e-05
## ... Procrustes: rmse 0.00018135 max resid 0.001186756
## ... Similar to previous best
## Run 6 stress 9.404251e-05
## ... Procrustes: rmse 0.0001821897 max resid 0.00092342
## ... Similar to previous best
## Run 7 stress 9.705609e-05
## ... Procrustes: rmse 0.0001778024 max resid 0.001134782
## ... Similar to previous best
## Run 8 stress 9.419114e-05
## ... Procrustes: rmse 0.0001671739 max resid 0.000859483
## ... Similar to previous best
## Run 9 stress 9.887112e-05
## ... Procrustes: rmse 0.0001836333 max resid 0.0008795596
## ... Similar to previous best
## Run 10 stress 8.777573e-05
## ... Procrustes: rmse 0.0001817728 max resid 0.00117603
## ... Similar to previous best
## Run 11 stress 9.298384e-05
## ... Procrustes: rmse 0.0001786016 max resid 0.001064788
## ... Similar to previous best
## Run 12 stress 9.770213e-05
## ... Procrustes: rmse 0.00018721 max resid 0.001187054
## ... Similar to previous best
## Run 13 stress 9.262476e-05
## ... Procrustes: rmse 0.0001837213 max resid 0.001197153
## ... Similar to previous best
## Run 14 stress 9.967561e-05
## ... Procrustes: rmse 0.0001982104 max resid 0.001278432
## ... Similar to previous best
## Run 15 stress 9.63867e-05
## ... Procrustes: rmse 0.0001847329 max resid 0.001164215
## ... Similar to previous best
## Run 16 stress 9.435399e-05
## ... Procrustes: rmse 0.0001891634 max resid 0.001216534
## ... Similar to previous best
## Run 17 stress 9.725791e-05
## ... Procrustes: rmse 0.0001898888 max resid 0.001210536
## ... Similar to previous best
## Run 18 stress 9.591623e-05
## ... Procrustes: rmse 0.0001809856 max resid 0.001056011
## ... Similar to previous best
## Run 19 stress 9.346098e-05
## ... Procrustes: rmse 0.0001873273 max resid 0.00120528
## ... Similar to previous best
## Run 20 stress 9.143962e-05
## ... Procrustes: rmse 0.0001694691 max resid 0.000911081
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.314284e-05
## ... Procrustes: rmse 0.0001525683 max resid 0.0007071475
## ... Similar to previous best
## Run 2 stress 8.617958e-05
## ... Procrustes: rmse 0.0001386558 max resid 0.0005204851
## ... Similar to previous best
## Run 3 stress 9.844571e-05
## ... Procrustes: rmse 0.000158191 max resid 0.0006689462
## ... Similar to previous best
## Run 4 stress 9.934764e-05
## ... Procrustes: rmse 0.0001584433 max resid 0.0007665075
## ... Similar to previous best
## Run 5 stress 9.700439e-05
## ... Procrustes: rmse 0.0001426505 max resid 0.0004993978
## ... Similar to previous best
## Run 6 stress 8.76813e-05
## ... Procrustes: rmse 0.0001376287 max resid 0.0005870343
## ... Similar to previous best
## Run 7 stress 8.998935e-05
## ... Procrustes: rmse 0.0001470729 max resid 0.0005132984
## ... Similar to previous best
## Run 8 stress 9.595722e-05
## ... Procrustes: rmse 0.0001565644 max resid 0.0007258068
## ... Similar to previous best
## Run 9 stress 9.312415e-05
## ... Procrustes: rmse 0.0001608595 max resid 0.0008114967
## ... Similar to previous best
## Run 10 stress 8.720205e-05
## ... Procrustes: rmse 0.0001261678 max resid 0.0003998242
## ... Similar to previous best
## Run 11 stress 8.883454e-05
## ... Procrustes: rmse 0.0001530222 max resid 0.0006981399
## ... Similar to previous best
## Run 12 stress 9.490853e-05
## ... Procrustes: rmse 0.0001613058 max resid 0.0006562207
## ... Similar to previous best
## Run 13 stress 8.914309e-05
## ... Procrustes: rmse 0.000135389 max resid 0.0004877766
## ... Similar to previous best
## Run 14 stress 9.260007e-05
## ... Procrustes: rmse 0.0001604979 max resid 0.0006762393
## ... Similar to previous best
## Run 15 stress 9.116654e-05
## ... Procrustes: rmse 0.0001435535 max resid 0.0005730897
## ... Similar to previous best
## Run 16 stress 9.901248e-05
## ... Procrustes: rmse 0.0001641883 max resid 0.0007650489
## ... Similar to previous best
## Run 17 stress 9.259275e-05
## ... Procrustes: rmse 0.0001445003 max resid 0.0007918013
## ... Similar to previous best
## Run 18 stress 8.84548e-05
## ... Procrustes: rmse 0.0001352404 max resid 0.0004965703
## ... Similar to previous best
## Run 19 stress 8.910437e-05
## ... Procrustes: rmse 0.0001505545 max resid 0.0007594997
## ... Similar to previous best
## Run 20 stress 9.561313e-05
## ... Procrustes: rmse 0.0001445956 max resid 0.0005503438
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.953798e-05
## ... Procrustes: rmse 0.0001250762 max resid 0.0006645469
## ... Similar to previous best
## Run 2 stress 9.897032e-05
## ... Procrustes: rmse 0.000168178 max resid 0.0007345901
## ... Similar to previous best
## Run 3 stress 8.738231e-05
## ... Procrustes: rmse 0.0001501629 max resid 0.0007506826
## ... Similar to previous best
## Run 4 stress 9.645719e-05
## ... Procrustes: rmse 0.000160689 max resid 0.0006844552
## ... Similar to previous best
## Run 5 stress 9.893987e-05
## ... Procrustes: rmse 0.0001619722 max resid 0.0007208596
## ... Similar to previous best
## Run 6 stress 9.720148e-05
## ... Procrustes: rmse 0.0001667237 max resid 0.0007254331
## ... Similar to previous best
## Run 7 stress 9.58258e-05
## ... Procrustes: rmse 0.0001649641 max resid 0.0006047028
## ... Similar to previous best
## Run 8 stress 9.024676e-05
## ... Procrustes: rmse 0.0001544715 max resid 0.0006548625
## ... Similar to previous best
## Run 9 stress 9.621605e-05
## ... Procrustes: rmse 0.0001606916 max resid 0.0009223183
## ... Similar to previous best
## Run 10 stress 9.266343e-05
## ... Procrustes: rmse 0.000152446 max resid 0.0006219466
## ... Similar to previous best
## Run 11 stress 9.425241e-05
## ... Procrustes: rmse 0.0001551398 max resid 0.000585227
## ... Similar to previous best
## Run 12 stress 8.813997e-05
## ... Procrustes: rmse 0.0001423901 max resid 0.0006058469
## ... Similar to previous best
## Run 13 stress 9.424037e-05
## ... Procrustes: rmse 0.0001622841 max resid 0.0006700055
## ... Similar to previous best
## Run 14 stress 9.309612e-05
## ... Procrustes: rmse 0.0001595226 max resid 0.0009292715
## ... Similar to previous best
## Run 15 stress 9.416644e-05
## ... Procrustes: rmse 0.0001450794 max resid 0.000740914
## ... Similar to previous best
## Run 16 stress 9.995661e-05
## ... Procrustes: rmse 0.000163182 max resid 0.000810608
## ... Similar to previous best
## Run 17 stress 9.473692e-05
## ... Procrustes: rmse 0.0001472164 max resid 0.0007717997
## ... Similar to previous best
## Run 18 stress 9.512078e-05
## ... Procrustes: rmse 0.0001540778 max resid 0.0006470059
## ... Similar to previous best
## Run 19 stress 9.764041e-05
## ... Procrustes: rmse 0.0001618791 max resid 0.0008202067
## ... Similar to previous best
## Run 20 stress 8.977656e-05
## ... Procrustes: rmse 0.0001572395 max resid 0.0008068601
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.176993e-05
## ... Procrustes: rmse 0.0001569411 max resid 0.0004923581
## ... Similar to previous best
## Run 2 stress 9.938426e-05
## ... Procrustes: rmse 0.0001744714 max resid 0.0008646477
## ... Similar to previous best
## Run 3 stress 8.900468e-05
## ... Procrustes: rmse 0.0001686778 max resid 0.000705338
## ... Similar to previous best
## Run 4 stress 9.100232e-05
## ... Procrustes: rmse 0.0001631245 max resid 0.0006433314
## ... Similar to previous best
## Run 5 stress 9.271507e-05
## ... Procrustes: rmse 0.0001743156 max resid 0.0007134257
## ... Similar to previous best
## Run 6 stress 9.994043e-05
## ... Procrustes: rmse 0.0001673623 max resid 0.0005236472
## ... Similar to previous best
## Run 7 stress 8.82342e-05
## ... Procrustes: rmse 0.0001626308 max resid 0.0006406149
## ... Similar to previous best
## Run 8 stress 9.64072e-05
## ... Procrustes: rmse 0.0001633871 max resid 0.0004982961
## ... Similar to previous best
## Run 9 stress 9.37467e-05
## ... Procrustes: rmse 0.0001724923 max resid 0.0006651361
## ... Similar to previous best
## Run 10 stress 9.538347e-05
## ... Procrustes: rmse 0.000167565 max resid 0.0006884888
## ... Similar to previous best
## Run 11 stress 9.268107e-05
## ... Procrustes: rmse 0.0001765603 max resid 0.000751054
## ... Similar to previous best
## Run 12 stress 9.490569e-05
## ... Procrustes: rmse 0.0001705477 max resid 0.0008227129
## ... Similar to previous best
## Run 13 stress 9.327552e-05
## ... Procrustes: rmse 0.0001525721 max resid 0.0005821558
## ... Similar to previous best
## Run 14 stress 9.522225e-05
## ... Procrustes: rmse 0.0001819285 max resid 0.0007130552
## ... Similar to previous best
## Run 15 stress 9.555489e-05
## ... Procrustes: rmse 0.0001704682 max resid 0.0005456251
## ... Similar to previous best
## Run 16 stress 9.021962e-05
## ... Procrustes: rmse 0.0001688163 max resid 0.0006451865
## ... Similar to previous best
## Run 17 stress 9.778557e-05
## ... Procrustes: rmse 0.0001919495 max resid 0.0008276186
## ... Similar to previous best
## Run 18 stress 9.463289e-05
## ... Procrustes: rmse 0.0001803474 max resid 0.0008128766
## ... Similar to previous best
## Run 19 stress 9.942718e-05
## ... Procrustes: rmse 0.0001871567 max resid 0.0007999196
## ... Similar to previous best
## Run 20 stress 9.976818e-05
## ... Procrustes: rmse 0.0001660427 max resid 0.000674745
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 8.292071e-05
## ... Procrustes: rmse 0.0001646441 max resid 0.001008409
## ... Similar to previous best
## Run 2 stress 9.053756e-05
## ... Procrustes: rmse 0.0001497594 max resid 0.0007220566
## ... Similar to previous best
## Run 3 stress 9.733385e-05
## ... Procrustes: rmse 0.0001682917 max resid 0.0008998098
## ... Similar to previous best
## Run 4 stress 9.105981e-05
## ... Procrustes: rmse 0.0001592523 max resid 0.0009892982
## ... Similar to previous best
## Run 5 stress 9.576138e-05
## ... Procrustes: rmse 0.0001785338 max resid 0.00101289
## ... Similar to previous best
## Run 6 stress 9.580732e-05
## ... Procrustes: rmse 0.000179181 max resid 0.001111062
## ... Similar to previous best
## Run 7 stress 9.390469e-05
## ... Procrustes: rmse 0.000178446 max resid 0.001022936
## ... Similar to previous best
## Run 8 stress 9.476021e-05
## ... Procrustes: rmse 0.0001746796 max resid 0.000758582
## ... Similar to previous best
## Run 9 stress 8.949982e-05
## ... Procrustes: rmse 0.0001687957 max resid 0.001058815
## ... Similar to previous best
## Run 10 stress 9.7765e-05
## ... Procrustes: rmse 0.0001651728 max resid 0.0009560604
## ... Similar to previous best
## Run 11 stress 9.410198e-05
## ... Procrustes: rmse 0.0001651964 max resid 0.0006974452
## ... Similar to previous best
## Run 12 stress 9.250919e-05
## ... Procrustes: rmse 0.0001730233 max resid 0.0009564419
## ... Similar to previous best
## Run 13 stress 9.424086e-05
## ... Procrustes: rmse 0.0001742444 max resid 0.001101114
## ... Similar to previous best
## Run 14 stress 9.942006e-05
## ... Procrustes: rmse 0.0001792702 max resid 0.001032862
## ... Similar to previous best
## Run 15 stress 9.530946e-05
## ... Procrustes: rmse 0.0001547875 max resid 0.000904823
## ... Similar to previous best
## Run 16 stress 9.756285e-05
## ... Procrustes: rmse 0.0001629167 max resid 0.0006162124
## ... Similar to previous best
## Run 17 stress 9.438744e-05
## ... Procrustes: rmse 0.0001712561 max resid 0.001010591
## ... Similar to previous best
## Run 18 stress 9.717785e-05
## ... Procrustes: rmse 0.0001750524 max resid 0.001120398
## ... Similar to previous best
## Run 19 stress 9.263621e-05
## ... Procrustes: rmse 0.0001600663 max resid 0.0006519888
## ... Similar to previous best
## Run 20 stress 9.796413e-05
## ... Procrustes: rmse 0.0001839554 max resid 0.001012526
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.332938e-05
## ... Procrustes: rmse 0.0001423511 max resid 0.0005998921
## ... Similar to previous best
## Run 2 stress 9.820404e-05
## ... Procrustes: rmse 0.00015979 max resid 0.0007882767
## ... Similar to previous best
## Run 3 stress 9.694442e-05
## ... Procrustes: rmse 0.0001530463 max resid 0.0006535466
## ... Similar to previous best
## Run 4 stress 8.271235e-05
## ... Procrustes: rmse 0.0001122218 max resid 0.0003492946
## ... Similar to previous best
## Run 5 stress 9.824076e-05
## ... Procrustes: rmse 0.0001595765 max resid 0.0008476137
## ... Similar to previous best
## Run 6 stress 8.685583e-05
## ... Procrustes: rmse 0.0001361459 max resid 0.0008122754
## ... Similar to previous best
## Run 7 stress 9.002127e-05
## ... Procrustes: rmse 0.0001452885 max resid 0.0005802017
## ... Similar to previous best
## Run 8 stress 8.853637e-05
## ... Procrustes: rmse 0.0001493444 max resid 0.0006852346
## ... Similar to previous best
## Run 9 stress 9.218078e-05
## ... Procrustes: rmse 0.0001486209 max resid 0.0005723627
## ... Similar to previous best
## Run 10 stress 7.342554e-05
## ... Procrustes: rmse 0.0001375158 max resid 0.0006450302
## ... Similar to previous best
## Run 11 stress 9.607061e-05
## ... Procrustes: rmse 0.000151752 max resid 0.0006111509
## ... Similar to previous best
## Run 12 stress 8.888982e-05
## ... Procrustes: rmse 0.0001426033 max resid 0.0006477908
## ... Similar to previous best
## Run 13 stress 9.558613e-05
## ... Procrustes: rmse 0.0001596161 max resid 0.0008840523
## ... Similar to previous best
## Run 14 stress 9.805032e-05
## ... Procrustes: rmse 0.0001450941 max resid 0.0007207976
## ... Similar to previous best
## Run 15 stress 9.823204e-05
## ... Procrustes: rmse 0.0001630558 max resid 0.0005398762
## ... Similar to previous best
## Run 16 stress 9.627809e-05
## ... Procrustes: rmse 0.0001526926 max resid 0.0006800156
## ... Similar to previous best
## Run 17 stress 9.044681e-05
## ... Procrustes: rmse 0.0001433337 max resid 0.0006748812
## ... Similar to previous best
## Run 18 stress 9.849024e-05
## ... Procrustes: rmse 0.0001531498 max resid 0.0004921265
## ... Similar to previous best
## Run 19 stress 9.303421e-05
## ... Procrustes: rmse 0.0001542314 max resid 0.0006190849
## ... Similar to previous best
## Run 20 stress 9.582818e-05
## ... Procrustes: rmse 0.0001493425 max resid 0.0006519312
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.863978e-05
## ... Procrustes: rmse 0.0001976422 max resid 0.0008990854
## ... Similar to previous best
## Run 2 stress 9.468572e-05
## ... Procrustes: rmse 0.0001970131 max resid 0.001252785
## ... Similar to previous best
## Run 3 stress 8.964282e-05
## ... Procrustes: rmse 0.000194152 max resid 0.001025989
## ... Similar to previous best
## Run 4 stress 9.7727e-05
## ... Procrustes: rmse 0.0002038204 max resid 0.001195048
## ... Similar to previous best
## Run 5 stress 9.640438e-05
## ... Procrustes: rmse 0.0002012676 max resid 0.001180226
## ... Similar to previous best
## Run 6 stress 9.24531e-05
## ... Procrustes: rmse 0.0001970826 max resid 0.00108177
## ... Similar to previous best
## Run 7 stress 9.887792e-05
## ... Procrustes: rmse 0.0001971265 max resid 0.00091411
## ... Similar to previous best
## Run 8 stress 9.089513e-05
## ... Procrustes: rmse 0.0001798707 max resid 0.0007747707
## ... Similar to previous best
## Run 9 stress 9.915118e-05
## ... Procrustes: rmse 0.0001963105 max resid 0.000783081
## ... Similar to previous best
## Run 10 stress 8.948078e-05
## ... Procrustes: rmse 0.000194616 max resid 0.001173585
## ... Similar to previous best
## Run 11 stress 7.468487e-05
## ... Procrustes: rmse 0.0001554162 max resid 0.0006308797
## ... Similar to previous best
## Run 12 stress 9.609251e-05
## ... Procrustes: rmse 0.0001954527 max resid 0.001010178
## ... Similar to previous best
## Run 13 stress 9.118097e-05
## ... Procrustes: rmse 0.00016941 max resid 0.0009381133
## ... Similar to previous best
## Run 14 stress 9.726257e-05
## ... Procrustes: rmse 0.0001833585 max resid 0.001053608
## ... Similar to previous best
## Run 15 stress 8.755507e-05
## ... Procrustes: rmse 0.0001595857 max resid 0.0008527108
## ... Similar to previous best
## Run 16 stress 8.375952e-05
## ... Procrustes: rmse 0.0001837398 max resid 0.001094152
## ... Similar to previous best
## Run 17 stress 9.44415e-05
## ... Procrustes: rmse 0.000200246 max resid 0.001247633
## ... Similar to previous best
## Run 18 stress 8.940751e-05
## ... Procrustes: rmse 0.0001795998 max resid 0.0007271841
## ... Similar to previous best
## Run 19 stress 8.873416e-05
## ... Procrustes: rmse 0.0001920964 max resid 0.001185693
## ... Similar to previous best
## Run 20 stress 8.319685e-05
## ... Procrustes: rmse 0.0001811019 max resid 0.0008914238
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.757001e-05
## ... Procrustes: rmse 0.0001853965 max resid 0.001092632
## ... Similar to previous best
## Run 2 stress 9.453763e-05
## ... Procrustes: rmse 0.0002027454 max resid 0.001301817
## ... Similar to previous best
## Run 3 stress 9.38688e-05
## ... Procrustes: rmse 0.0001783117 max resid 0.0007701467
## ... Similar to previous best
## Run 4 stress 9.567536e-05
## ... Procrustes: rmse 0.0001936517 max resid 0.000959014
## ... Similar to previous best
## Run 5 stress 8.481214e-05
## ... Procrustes: rmse 0.0001849685 max resid 0.001191662
## ... Similar to previous best
## Run 6 stress 9.909071e-05
## ... Procrustes: rmse 0.0002021888 max resid 0.001259856
## ... Similar to previous best
## Run 7 stress 9.325068e-05
## ... Procrustes: rmse 0.0001953224 max resid 0.001205792
## ... Similar to previous best
## Run 8 stress 9.423625e-05
## ... Procrustes: rmse 0.0002016055 max resid 0.001273471
## ... Similar to previous best
## Run 9 stress 8.521574e-05
## ... Procrustes: rmse 0.0001853893 max resid 0.001178392
## ... Similar to previous best
## Run 10 stress 9.91969e-05
## ... Procrustes: rmse 0.0001974456 max resid 0.001056181
## ... Similar to previous best
## Run 11 stress 9.738758e-05
## ... Procrustes: rmse 0.0002044362 max resid 0.001300388
## ... Similar to previous best
## Run 12 stress 9.399855e-05
## ... Procrustes: rmse 0.0002013634 max resid 0.001219525
## ... Similar to previous best
## Run 13 stress 8.951858e-05
## ... Procrustes: rmse 0.0001646951 max resid 0.0006011829
## ... Similar to previous best
## Run 14 stress 9.744844e-05
## ... Procrustes: rmse 0.0002085771 max resid 0.001331351
## ... Similar to previous best
## Run 15 stress 9.788644e-05
## ... Procrustes: rmse 0.0001820981 max resid 0.0007902638
## ... Similar to previous best
## Run 16 stress 9.06152e-05
## ... Procrustes: rmse 0.0001597005 max resid 0.0007122259
## ... Similar to previous best
## Run 17 stress 9.763373e-05
## ... Procrustes: rmse 0.0002062307 max resid 0.001071183
## ... Similar to previous best
## Run 18 stress 9.580241e-05
## ... Procrustes: rmse 0.0001958517 max resid 0.001259581
## ... Similar to previous best
## Run 19 stress 9.440154e-05
## ... Procrustes: rmse 0.0002044709 max resid 0.001297088
## ... Similar to previous best
## Run 20 stress 9.165545e-05
## ... Procrustes: rmse 0.0001900393 max resid 0.0009164142
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.130925e-05
## ... Procrustes: rmse 0.0001639041 max resid 0.0009553365
## ... Similar to previous best
## Run 2 stress 9.374097e-05
## ... Procrustes: rmse 0.0001659953 max resid 0.0008549286
## ... Similar to previous best
## Run 3 stress 9.784011e-05
## ... Procrustes: rmse 0.0001750741 max resid 0.0006160365
## ... Similar to previous best
## Run 4 stress 9.071235e-05
## ... Procrustes: rmse 0.0001596437 max resid 0.0004914712
## ... Similar to previous best
## Run 5 stress 8.373165e-05
## ... Procrustes: rmse 0.0001451953 max resid 0.0007619207
## ... Similar to previous best
## Run 6 stress 9.205811e-05
## ... Procrustes: rmse 0.0001596382 max resid 0.0007643853
## ... Similar to previous best
## Run 7 stress 8.9712e-05
## ... Procrustes: rmse 0.0001627812 max resid 0.0008149592
## ... Similar to previous best
## Run 8 stress 9.621993e-05
## ... Procrustes: rmse 0.0001653655 max resid 0.000634581
## ... Similar to previous best
## Run 9 stress 8.922069e-05
## ... Procrustes: rmse 0.0001585927 max resid 0.0005715313
## ... Similar to previous best
## Run 10 stress 9.155514e-05
## ... Procrustes: rmse 0.000161576 max resid 0.0005297578
## ... Similar to previous best
## Run 11 stress 8.879908e-05
## ... Procrustes: rmse 0.000156885 max resid 0.0006951626
## ... Similar to previous best
## Run 12 stress 9.24787e-05
## ... Procrustes: rmse 0.0001501981 max resid 0.0007374116
## ... Similar to previous best
## Run 13 stress 9.907401e-05
## ... Procrustes: rmse 0.000163998 max resid 0.0007818867
## ... Similar to previous best
## Run 14 stress 9.208765e-05
## ... Procrustes: rmse 0.0001535368 max resid 0.0008985849
## ... Similar to previous best
## Run 15 stress 7.33595e-05
## ... Procrustes: rmse 0.0001447161 max resid 0.0007508668
## ... Similar to previous best
## Run 16 stress 9.538816e-05
## ... Procrustes: rmse 0.0001693383 max resid 0.0006788203
## ... Similar to previous best
## Run 17 stress 9.887238e-05
## ... Procrustes: rmse 0.0001704297 max resid 0.0007917928
## ... Similar to previous best
## Run 18 stress 9.789994e-05
## ... Procrustes: rmse 0.0001666522 max resid 0.0009223587
## ... Similar to previous best
## Run 19 stress 9.165087e-05
## ... Procrustes: rmse 0.0001648073 max resid 0.0009122313
## ... Similar to previous best
## Run 20 stress 9.239366e-05
## ... Procrustes: rmse 0.0001572819 max resid 0.0006177112
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 8.941608e-05
## ... Procrustes: rmse 0.0001837354 max resid 0.0008906608
## ... Similar to previous best
## Run 2 stress 9.306644e-05
## ... Procrustes: rmse 0.0002106607 max resid 0.001105085
## ... Similar to previous best
## Run 3 stress 8.459655e-05
## ... Procrustes: rmse 0.0002066391 max resid 0.001094598
## ... Similar to previous best
## Run 4 stress 9.355981e-05
## ... Procrustes: rmse 0.000206327 max resid 0.001003315
## ... Similar to previous best
## Run 5 stress 9.280859e-05
## ... Procrustes: rmse 0.0002162015 max resid 0.0009488946
## ... Similar to previous best
## Run 6 stress 9.579913e-05
## ... Procrustes: rmse 0.0002147183 max resid 0.001192619
## ... Similar to previous best
## Run 7 stress 9.471056e-05
## ... Procrustes: rmse 0.0001794488 max resid 0.0009127528
## ... Similar to previous best
## Run 8 stress 9.322145e-05
## ... Procrustes: rmse 0.000211718 max resid 0.001076408
## ... Similar to previous best
## Run 9 stress 9.447091e-05
## ... Procrustes: rmse 0.0002008526 max resid 0.001018116
## ... Similar to previous best
## Run 10 stress 9.531993e-05
## ... Procrustes: rmse 0.0001909259 max resid 0.000766897
## ... Similar to previous best
## Run 11 stress 9.291797e-05
## ... Procrustes: rmse 0.0002035065 max resid 0.0009886107
## ... Similar to previous best
## Run 12 stress 9.880837e-05
## ... Procrustes: rmse 0.0002208746 max resid 0.00119455
## ... Similar to previous best
## Run 13 stress 9.972902e-05
## ... Procrustes: rmse 0.0002158097 max resid 0.001172429
## ... Similar to previous best
## Run 14 stress 9.798934e-05
## ... Procrustes: rmse 0.0002165157 max resid 0.001259317
## ... Similar to previous best
## Run 15 stress 9.245476e-05
## ... Procrustes: rmse 0.0002074022 max resid 0.000931226
## ... Similar to previous best
## Run 16 stress 9.165221e-05
## ... Procrustes: rmse 0.0002089308 max resid 0.00119207
## ... Similar to previous best
## Run 17 stress 9.652448e-05
## ... Procrustes: rmse 0.0002048194 max resid 0.001131656
## ... Similar to previous best
## Run 18 stress 9.599436e-05
## ... Procrustes: rmse 0.0002059033 max resid 0.00111306
## ... Similar to previous best
## Run 19 stress 9.020018e-05
## ... Procrustes: rmse 0.0001922931 max resid 0.0009747292
## ... Similar to previous best
## Run 20 stress 9.639381e-05
## ... Procrustes: rmse 0.0001808645 max resid 0.0009034467
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.675274e-05
## ... Procrustes: rmse 0.0001474127 max resid 0.0006114136
## ... Similar to previous best
## Run 2 stress 8.710806e-05
## ... Procrustes: rmse 0.0001211781 max resid 0.000483406
## ... Similar to previous best
## Run 3 stress 8.83613e-05
## ... Procrustes: rmse 0.0001386906 max resid 0.000658031
## ... Similar to previous best
## Run 4 stress 9.814584e-05
## ... Procrustes: rmse 0.0001491844 max resid 0.0007598175
## ... Similar to previous best
## Run 5 stress 8.982452e-05
## ... Procrustes: rmse 0.0001377242 max resid 0.0006431465
## ... Similar to previous best
## Run 6 stress 9.426326e-05
## ... Procrustes: rmse 0.0001424673 max resid 0.0006258483
## ... Similar to previous best
## Run 7 stress 9.142398e-05
## ... Procrustes: rmse 0.0001486089 max resid 0.0005396711
## ... Similar to previous best
## Run 8 stress 9.834186e-05
## ... Procrustes: rmse 0.0001482625 max resid 0.0007411069
## ... Similar to previous best
## Run 9 stress 8.782967e-05
## ... Procrustes: rmse 0.0001447565 max resid 0.0006508951
## ... Similar to previous best
## Run 10 stress 9.904619e-05
## ... Procrustes: rmse 0.0001586379 max resid 0.0008285393
## ... Similar to previous best
## Run 11 stress 9.798492e-05
## ... Procrustes: rmse 0.0001466893 max resid 0.0007151414
## ... Similar to previous best
## Run 12 stress 9.488424e-05
## ... Procrustes: rmse 0.0001616092 max resid 0.0007099414
## ... Similar to previous best
## Run 13 stress 9.822071e-05
## ... Procrustes: rmse 0.000153158 max resid 0.0005491903
## ... Similar to previous best
## Run 14 stress 9.414095e-05
## ... Procrustes: rmse 0.0001485736 max resid 0.000693955
## ... Similar to previous best
## Run 15 stress 7.687833e-05
## ... Procrustes: rmse 0.0001284169 max resid 0.0003425519
## ... Similar to previous best
## Run 16 stress 8.895631e-05
## ... Procrustes: rmse 0.0001423911 max resid 0.0006102359
## ... Similar to previous best
## Run 17 stress 9.959534e-05
## ... Procrustes: rmse 0.0001549481 max resid 0.0006427647
## ... Similar to previous best
## Run 18 stress 9.330242e-05
## ... Procrustes: rmse 0.0001409305 max resid 0.0005454801
## ... Similar to previous best
## Run 19 stress 9.854155e-05
## ... Procrustes: rmse 0.0001565172 max resid 0.0007147049
## ... Similar to previous best
## Run 20 stress 9.224031e-05
## ... Procrustes: rmse 0.0001510563 max resid 0.000622836
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.163784e-05
## ... Procrustes: rmse 0.0001554733 max resid 0.0006231112
## ... Similar to previous best
## Run 2 stress 9.499448e-05
## ... Procrustes: rmse 0.0001646863 max resid 0.000512596
## ... Similar to previous best
## Run 3 stress 9.319796e-05
## ... Procrustes: rmse 0.000160228 max resid 0.0006738383
## ... Similar to previous best
## Run 4 stress 8.755533e-05
## ... Procrustes: rmse 0.000137528 max resid 0.0004393724
## ... Similar to previous best
## Run 5 stress 9.141695e-05
## ... Procrustes: rmse 0.0001574477 max resid 0.0007714386
## ... Similar to previous best
## Run 6 stress 9.756116e-05
## ... Procrustes: rmse 0.0001633256 max resid 0.000666908
## ... Similar to previous best
## Run 7 stress 9.656383e-05
## ... Procrustes: rmse 0.0001639304 max resid 0.000769515
## ... Similar to previous best
## Run 8 stress 9.959298e-05
## ... Procrustes: rmse 0.0001649451 max resid 0.0006951603
## ... Similar to previous best
## Run 9 stress 9.092127e-05
## ... Procrustes: rmse 0.0001589308 max resid 0.0005164822
## ... Similar to previous best
## Run 10 stress 9.754567e-05
## ... Procrustes: rmse 0.0001595415 max resid 0.0006085249
## ... Similar to previous best
## Run 11 stress 9.28516e-05
## ... Procrustes: rmse 0.0001527778 max resid 0.00041233
## ... Similar to previous best
## Run 12 stress 9.732367e-05
## ... Procrustes: rmse 0.0001456873 max resid 0.0003506201
## ... Similar to previous best
## Run 13 stress 8.410429e-05
## ... Procrustes: rmse 0.000148631 max resid 0.00052961
## ... Similar to previous best
## Run 14 stress 9.283209e-05
## ... Procrustes: rmse 0.0001522513 max resid 0.0005156826
## ... Similar to previous best
## Run 15 stress 9.286035e-05
## ... Procrustes: rmse 0.0001636369 max resid 0.0005702708
## ... Similar to previous best
## Run 16 stress 9.781194e-05
## ... Procrustes: rmse 0.0001666595 max resid 0.0006708884
## ... Similar to previous best
## Run 17 stress 9.049256e-05
## ... Procrustes: rmse 0.0001588367 max resid 0.000493547
## ... Similar to previous best
## Run 18 stress 8.199813e-05
## ... Procrustes: rmse 0.0001399481 max resid 0.0005576346
## ... Similar to previous best
## Run 19 stress 8.250146e-05
## ... Procrustes: rmse 0.000136241 max resid 0.0004024118
## ... Similar to previous best
## Run 20 stress 9.571733e-05
## ... Procrustes: rmse 0.0001496826 max resid 0.0004840441
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.744838e-05
## ... Procrustes: rmse 0.0001694317 max resid 0.000744948
## ... Similar to previous best
## Run 2 stress 9.08163e-05
## ... Procrustes: rmse 0.0001770082 max resid 0.0008968553
## ... Similar to previous best
## Run 3 stress 9.091627e-05
## ... Procrustes: rmse 0.0001683905 max resid 0.0008076063
## ... Similar to previous best
## Run 4 stress 9.054761e-05
## ... Procrustes: rmse 0.0001759863 max resid 0.0009284688
## ... Similar to previous best
## Run 5 stress 9.918251e-05
## ... Procrustes: rmse 0.0001947961 max resid 0.001057226
## ... Similar to previous best
## Run 6 stress 9.746803e-05
## ... Procrustes: rmse 0.000179102 max resid 0.0007914789
## ... Similar to previous best
## Run 7 stress 9.43766e-05
## ... Procrustes: rmse 0.0001856724 max resid 0.0007778767
## ... Similar to previous best
## Run 8 stress 9.621068e-05
## ... Procrustes: rmse 0.0001824436 max resid 0.0006879437
## ... Similar to previous best
## Run 9 stress 8.361984e-05
## ... Procrustes: rmse 0.0001679514 max resid 0.0007159564
## ... Similar to previous best
## Run 10 stress 9.089442e-05
## ... Procrustes: rmse 0.0001640219 max resid 0.0008387327
## ... Similar to previous best
## Run 11 stress 9.22039e-05
## ... Procrustes: rmse 0.0001735072 max resid 0.000949042
## ... Similar to previous best
## Run 12 stress 9.270314e-05
## ... Procrustes: rmse 0.0001711752 max resid 0.001001346
## ... Similar to previous best
## Run 13 stress 9.373353e-05
## ... Procrustes: rmse 0.0001792234 max resid 0.0009369313
## ... Similar to previous best
## Run 14 stress 9.570845e-05
## ... Procrustes: rmse 0.0001688608 max resid 0.0007430867
## ... Similar to previous best
## Run 15 stress 9.931906e-05
## ... Procrustes: rmse 0.0001795798 max resid 0.0009777482
## ... Similar to previous best
## Run 16 stress 9.936983e-05
## ... Procrustes: rmse 0.0001840853 max resid 0.0008745316
## ... Similar to previous best
## Run 17 stress 7.460065e-05
## ... Procrustes: rmse 0.0001526369 max resid 0.0008466613
## ... Similar to previous best
## Run 18 stress 9.990659e-05
## ... Procrustes: rmse 0.0001922711 max resid 0.001027854
## ... Similar to previous best
## Run 19 stress 9.476789e-05
## ... Procrustes: rmse 0.0001762121 max resid 0.000721772
## ... Similar to previous best
## Run 20 stress 9.178347e-05
## ... Procrustes: rmse 0.0001626659 max resid 0.0004904969
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 8.991263e-05
## ... Procrustes: rmse 0.0001478254 max resid 0.0005231353
## ... Similar to previous best
## Run 2 stress 9.865867e-05
## ... Procrustes: rmse 0.0001498493 max resid 0.0004562479
## ... Similar to previous best
## Run 3 stress 9.908485e-05
## ... Procrustes: rmse 0.0001554751 max resid 0.000548006
## ... Similar to previous best
## Run 4 stress 9.343688e-05
## ... Procrustes: rmse 0.0001517385 max resid 0.000570355
## ... Similar to previous best
## Run 5 stress 8.629799e-05
## ... Procrustes: rmse 0.0001364997 max resid 0.000509679
## ... Similar to previous best
## Run 6 stress 9.995289e-05
## ... Procrustes: rmse 0.000159967 max resid 0.0006399464
## ... Similar to previous best
## Run 7 stress 9.700121e-05
## ... Procrustes: rmse 0.0001503632 max resid 0.0008089796
## ... Similar to previous best
## Run 8 stress 9.123543e-05
## ... Procrustes: rmse 0.000147353 max resid 0.0007493319
## ... Similar to previous best
## Run 9 stress 9.900296e-05
## ... Procrustes: rmse 0.000153357 max resid 0.0006162373
## ... Similar to previous best
## Run 10 stress 9.305477e-05
## ... Procrustes: rmse 0.0001560069 max resid 0.0006535648
## ... Similar to previous best
## Run 11 stress 9.835633e-05
## ... Procrustes: rmse 0.0001541081 max resid 0.000540582
## ... Similar to previous best
## Run 12 stress 8.880932e-05
## ... Procrustes: rmse 0.0001544345 max resid 0.000518712
## ... Similar to previous best
## Run 13 stress 9.836139e-05
## ... Procrustes: rmse 0.0001752034 max resid 0.0006316572
## ... Similar to previous best
## Run 14 stress 9.870466e-05
## ... Procrustes: rmse 0.0001800887 max resid 0.0006788707
## ... Similar to previous best
## Run 15 stress 9.183838e-05
## ... Procrustes: rmse 0.0001384013 max resid 0.0006547405
## ... Similar to previous best
## Run 16 stress 9.268203e-05
## ... Procrustes: rmse 0.000154087 max resid 0.0004575641
## ... Similar to previous best
## Run 17 stress 8.753984e-05
## ... Procrustes: rmse 0.0001473285 max resid 0.0007263853
## ... Similar to previous best
## Run 18 stress 8.997578e-05
## ... Procrustes: rmse 0.0001537794 max resid 0.0006338977
## ... Similar to previous best
## Run 19 stress 9.81983e-05
## ... Procrustes: rmse 0.0001468926 max resid 0.0005781092
## ... Similar to previous best
## Run 20 stress 8.264598e-05
## ... Procrustes: rmse 0.0001508773 max resid 0.0007577829
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 9.928109e-05
## ... Procrustes: rmse 0.0001901847 max resid 0.0006640892
## ... Similar to previous best
## Run 2 stress 9.861233e-05
## ... Procrustes: rmse 0.0002046389 max resid 0.0008075977
## ... Similar to previous best
## Run 3 stress 9.312531e-05
## ... Procrustes: rmse 0.000179873 max resid 0.0008867971
## ... Similar to previous best
## Run 4 stress 9.89407e-05
## ... Procrustes: rmse 0.0002005398 max resid 0.001088059
## ... Similar to previous best
## Run 5 stress 9.782362e-05
## ... Procrustes: rmse 0.0002261366 max resid 0.00122972
## ... Similar to previous best
## Run 6 stress 9.788952e-05
## ... Procrustes: rmse 0.0002265095 max resid 0.001222707
## ... Similar to previous best
## Run 7 stress 9.912394e-05
## ... Procrustes: rmse 0.0001823685 max resid 0.001112316
## ... Similar to previous best
## Run 8 stress 9.678591e-05
## ... Procrustes: rmse 0.0001966802 max resid 0.0009612072
## ... Similar to previous best
## Run 9 stress 8.871242e-05
## ... Procrustes: rmse 0.0001865244 max resid 0.0009401972
## ... Similar to previous best
## Run 10 stress 9.440076e-05
## ... Procrustes: rmse 0.0002265606 max resid 0.001269255
## ... Similar to previous best
## Run 11 stress 9.814904e-05
## ... Procrustes: rmse 0.0002354599 max resid 0.001143231
## ... Similar to previous best
## Run 12 stress 9.115829e-05
## ... Procrustes: rmse 0.0001736362 max resid 0.0006847871
## ... Similar to previous best
## Run 13 stress 8.011186e-05
## ... Procrustes: rmse 0.0001793137 max resid 0.0009517767
## ... Similar to previous best
## Run 14 stress 9.856441e-05
## ... Procrustes: rmse 0.0001927279 max resid 0.0008431198
## ... Similar to previous best
## Run 15 stress 8.599339e-05
## ... Procrustes: rmse 0.0001269807 max resid 0.0005250521
## ... Similar to previous best
## Run 16 stress 9.415137e-05
## ... Procrustes: rmse 0.000194021 max resid 0.001073199
## ... Similar to previous best
## Run 17 stress 9.368113e-05
## ... Procrustes: rmse 0.000195539 max resid 0.001088761
## ... Similar to previous best
## Run 18 stress 9.449807e-05
## ... Procrustes: rmse 0.0001520591 max resid 0.0005189785
## ... Similar to previous best
## Run 19 stress 9.338985e-05
## ... Procrustes: rmse 0.0001873373 max resid 0.0006348992
## ... Similar to previous best
## Run 20 stress 9.03748e-05
## ... Procrustes: rmse 0.0001843697 max resid 0.0009679146
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0001042102
## ... Procrustes: rmse 0.0004061777 max resid 0.002073754
## ... Similar to previous best
## Run 2 stress 9.94146e-05
## ... Procrustes: rmse 0.000352511 max resid 0.001585636
## ... Similar to previous best
## Run 3 stress 0.0001036477
## ... Procrustes: rmse 0.0003894654 max resid 0.002758619
## ... Similar to previous best
## Run 4 stress 9.896826e-05
## ... Procrustes: rmse 0.0003612628 max resid 0.002123
## ... Similar to previous best
## Run 5 stress 0.0001140364
## ... Procrustes: rmse 0.0004485065 max resid 0.002889977
## ... Similar to previous best
## Run 6 stress 9.69481e-05
## ... Procrustes: rmse 0.0003380018 max resid 0.001478861
## ... Similar to previous best
## Run 7 stress 0.0001239074
## ... Procrustes: rmse 0.0004627741 max resid 0.002888351
## ... Similar to previous best
## Run 8 stress 0.000104301
## ... Procrustes: rmse 0.0004127469 max resid 0.002557512
## ... Similar to previous best
## Run 9 stress 0.0001042099
## ... Procrustes: rmse 0.0003938876 max resid 0.002767697
## ... Similar to previous best
## Run 10 stress 0.000167714
## ... Procrustes: rmse 0.0005297217 max resid 0.003775653
## ... Similar to previous best
## Run 11 stress 0.0001115175
## ... Procrustes: rmse 0.0004342985 max resid 0.002698302
## ... Similar to previous best
## Run 12 stress 0.0001069778
## ... Procrustes: rmse 0.0004253061 max resid 0.00240873
## ... Similar to previous best
## Run 13 stress 0.0001127099
## ... Procrustes: rmse 0.000420037 max resid 0.002870787
## ... Similar to previous best
## Run 14 stress 8.570445e-05
## ... Procrustes: rmse 0.0003040533 max resid 0.001814368
## ... Similar to previous best
## Run 15 stress 0.0001143883
## ... Procrustes: rmse 0.0004438942 max resid 0.002562706
## ... Similar to previous best
## Run 16 stress 0.0001135705
## ... Procrustes: rmse 0.0004095298 max resid 0.002867028
## ... Similar to previous best
## Run 17 stress 0.0001200141
## ... Procrustes: rmse 0.0004506632 max resid 0.002752666
## ... Similar to previous best
## Run 18 stress 0.000111803
## ... Procrustes: rmse 0.0004349329 max resid 0.002664416
## ... Similar to previous best
## Run 19 stress 0.0001083401
## ... Procrustes: rmse 0.0004271084 max resid 0.002293266
## ... Similar to previous best
## Run 20 stress 0.0001107156
## ... Procrustes: rmse 0.0004347005 max resid 0.002594828
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004054395
## ... Procrustes: rmse 0.004676715 max resid 0.01356454
## Run 2 stress 0.0005082604
## Run 3 stress 0.0004280112
## ... Procrustes: rmse 0.004990536 max resid 0.01377029
## Run 4 stress 0.0004174721
## ... Procrustes: rmse 0.004771636 max resid 0.01247505
## Run 5 stress 0.0004501231
## ... Procrustes: rmse 0.004992105 max resid 0.01680338
## Run 6 stress 0.0005188257
## Run 7 stress 0.0004800901
## ... Procrustes: rmse 0.005044465 max resid 0.01408516
## Run 8 stress 0.0004609701
## ... Procrustes: rmse 0.005095727 max resid 0.01770976
## Run 9 stress 0.0004409208
## ... Procrustes: rmse 0.005070787 max resid 0.01507456
## Run 10 stress 0.0004810374
## ... Procrustes: rmse 0.005176887 max resid 0.01507412
## Run 11 stress 0.0004990449
## ... Procrustes: rmse 0.005464092 max resid 0.01339958
## Run 12 stress 0.0004792089
## ... Procrustes: rmse 0.005529758 max resid 0.01809657
## Run 13 stress 0.0006216051
## Run 14 stress 0.0004399177
## ... Procrustes: rmse 0.0049744 max resid 0.01187789
## Run 15 stress 0.0004277511
## ... Procrustes: rmse 0.004882496 max resid 0.0141324
## Run 16 stress 0.0005071531
## Run 17 stress 0.0005416278
## Run 18 stress 0.0005301443
## Run 19 stress 0.0004718996
## ... Procrustes: rmse 0.005223629 max resid 0.01485867
## Run 20 stress 0.0005888216
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0003770903
## ... Procrustes: rmse 0.004647337 max resid 0.01277051
## Run 2 stress 0.0003595577
## ... Procrustes: rmse 0.004466133 max resid 0.0115391
## Run 3 stress 0.0006634805
## Run 4 stress 0.0006770347
## Run 5 stress 0.0004441678
## ... Procrustes: rmse 0.004853688 max resid 0.01298301
## Run 6 stress 0.0003498852
## ... Procrustes: rmse 0.004342325 max resid 0.009651038
## ... Similar to previous best
## Run 7 stress 0.0004049592
## ... Procrustes: rmse 0.004712413 max resid 0.01214893
## Run 8 stress 0.0007520971
## Run 9 stress 0.0004388818
## ... Procrustes: rmse 0.00487844 max resid 0.01374855
## Run 10 stress 0.0005211211
## Run 11 stress 0.0004787295
## ... Procrustes: rmse 0.004842006 max resid 0.01478272
## Run 12 stress 0.0006515084
## Run 13 stress 0.0006826402
## Run 14 stress 0.0005924982
## Run 15 stress 0.0004114997
## ... Procrustes: rmse 0.004798863 max resid 0.01258189
## Run 16 stress 0.0004281542
## ... Procrustes: rmse 0.004695837 max resid 0.01135825
## Run 17 stress 0.0005549326
## Run 18 stress 0.0003579141
## ... Procrustes: rmse 0.004333386 max resid 0.00984619
## ... Similar to previous best
## Run 19 stress 0.0004275255
## ... Procrustes: rmse 0.00494641 max resid 0.0135284
## Run 20 stress 0.0005938215
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004447637
## ... Procrustes: rmse 0.005078614 max resid 0.01613304
## Run 2 stress 0.0004033047
## ... Procrustes: rmse 0.004892495 max resid 0.01381883
## Run 3 stress 0.0005755525
## Run 4 stress 0.0004064063
## ... Procrustes: rmse 0.004795635 max resid 0.01242594
## Run 5 stress 0.0004762347
## ... Procrustes: rmse 0.005164971 max resid 0.02205592
## Run 6 stress 0.0006007723
## Run 7 stress 0.0004128966
## ... Procrustes: rmse 0.004511226 max resid 0.01001045
## Run 8 stress 0.0004368608
## ... Procrustes: rmse 0.004929261 max resid 0.01115851
## Run 9 stress 0.0004084051
## ... Procrustes: rmse 0.004661014 max resid 0.01171382
## Run 10 stress 0.001269329
## Run 11 stress 0.0004188099
## ... Procrustes: rmse 0.004764357 max resid 0.01453556
## Run 12 stress 0.0006148549
## Run 13 stress 0.000608749
## Run 14 stress 0.0005076747
## Run 15 stress 0.0005376589
## Run 16 stress 0.0006209523
## Run 17 stress 0.0005245442
## Run 18 stress 0.0004501203
## ... Procrustes: rmse 0.005044045 max resid 0.01586529
## Run 19 stress 0.0004712087
## ... Procrustes: rmse 0.005024777 max resid 0.01140351
## Run 20 stress 0.0004269802
## ... Procrustes: rmse 0.004760687 max resid 0.01099811
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0005749425
## Run 2 stress 0.0004620371
## ... Procrustes: rmse 0.005062215 max resid 0.01387258
## Run 3 stress 0.0006354683
## Run 4 stress 0.0004485594
## ... Procrustes: rmse 0.004762857 max resid 0.01124355
## Run 5 stress 0.0003695395
## ... Procrustes: rmse 0.004447122 max resid 0.009093954
## ... Similar to previous best
## Run 6 stress 0.0004044759
## ... Procrustes: rmse 0.004524124 max resid 0.01587895
## Run 7 stress 0.0006280256
## Run 8 stress 0.0005507887
## Run 9 stress 0.0005085121
## Run 10 stress 0.0004221184
## ... Procrustes: rmse 0.004849176 max resid 0.01181672
## Run 11 stress 0.0006176691
## Run 12 stress 0.0003491385
## ... Procrustes: rmse 0.004352353 max resid 0.01093186
## Run 13 stress 0.0004344122
## ... Procrustes: rmse 0.00477226 max resid 0.01124328
## Run 14 stress 0.0004069835
## ... Procrustes: rmse 0.00479846 max resid 0.0139211
## Run 15 stress 0.0005679287
## Run 16 stress 0.0004479994
## ... Procrustes: rmse 0.005179643 max resid 0.01592984
## Run 17 stress 0.0005469223
## Run 18 stress 0.0005964285
## Run 19 stress 0.0003946412
## ... Procrustes: rmse 0.004552976 max resid 0.01107987
## Run 20 stress 0.0005981234
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.001020822
## Run 2 stress 0.0006444083
## Run 3 stress 0.0004469618
## ... Procrustes: rmse 0.005075876 max resid 0.01537029
## Run 4 stress 0.0004723572
## ... Procrustes: rmse 0.005179591 max resid 0.0180244
## Run 5 stress 0.000871568
## Run 6 stress 0.0004267588
## ... Procrustes: rmse 0.004685492 max resid 0.01408312
## Run 7 stress 0.0004450017
## ... Procrustes: rmse 0.004849129 max resid 0.01216869
## Run 8 stress 0.00062076
## Run 9 stress 0.000499895
## ... Procrustes: rmse 0.005518242 max resid 0.0156967
## Run 10 stress 0.0004544183
## ... Procrustes: rmse 0.005000542 max resid 0.01421862
## Run 11 stress 0.0003944085
## ... Procrustes: rmse 0.004785272 max resid 0.01191196
## Run 12 stress 0.0004193852
## ... Procrustes: rmse 0.004763153 max resid 0.01356063
## Run 13 stress 0.0004010218
## ... Procrustes: rmse 0.004554851 max resid 0.01091679
## Run 14 stress 0.0004299752
## ... Procrustes: rmse 0.004965562 max resid 0.01203504
## Run 15 stress 0.0004098858
## ... Procrustes: rmse 0.004775098 max resid 0.01452086
## Run 16 stress 0.0004102211
## ... Procrustes: rmse 0.004758659 max resid 0.01438049
## Run 17 stress 0.0003788778
## ... Procrustes: rmse 0.004844282 max resid 0.013958
## Run 18 stress 0.0004917145
## ... Procrustes: rmse 0.005279683 max resid 0.01222148
## Run 19 stress 0.0008179319
## Run 20 stress 0.0004495055
## ... Procrustes: rmse 0.005361393 max resid 0.01561308
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004674618
## ... Procrustes: rmse 0.004993136 max resid 0.01404296
## Run 2 stress 0.0005291951
## Run 3 stress 0.0004861855
## ... Procrustes: rmse 0.005080865 max resid 0.01607966
## Run 4 stress 0.0005611245
## Run 5 stress 0.0004406592
## ... Procrustes: rmse 0.004866496 max resid 0.01324931
## Run 6 stress 0.0005615114
## Run 7 stress 0.0005579774
## Run 8 stress 0.000455977
## ... Procrustes: rmse 0.004956591 max resid 0.01065272
## Run 9 stress 0.0009508129
## Run 10 stress 0.000451864
## ... Procrustes: rmse 0.005054561 max resid 0.01316836
## Run 11 stress 0.0005998938
## Run 12 stress 0.0004366676
## ... Procrustes: rmse 0.00496106 max resid 0.01772132
## Run 13 stress 0.0004610555
## ... Procrustes: rmse 0.00528373 max resid 0.01265275
## Run 14 stress 0.0004903739
## ... Procrustes: rmse 0.005196814 max resid 0.01870899
## Run 15 stress 0.0004200443
## ... Procrustes: rmse 0.005120945 max resid 0.01469275
## Run 16 stress 0.0004318964
## ... Procrustes: rmse 0.005042318 max resid 0.01593559
## Run 17 stress 0.0004448968
## ... Procrustes: rmse 0.00502414 max resid 0.01125154
## Run 18 stress 0.0004420372
## ... Procrustes: rmse 0.005051202 max resid 0.01423761
## Run 19 stress 0.0003928807
## ... Procrustes: rmse 0.004535274 max resid 0.01021824
## Run 20 stress 0.0004641952
## ... Procrustes: rmse 0.005423835 max resid 0.01680702
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.001306396
## Run 2 stress 0.0004425689
## ... Procrustes: rmse 0.005008464 max resid 0.01766338
## Run 3 stress 0.001022519
## Run 4 stress 0.0008608258
## Run 5 stress 0.0004855321
## ... Procrustes: rmse 0.006074671 max resid 0.02484161
## Run 6 stress 0.0004107912
## ... Procrustes: rmse 0.004614349 max resid 0.02015461
## Run 7 stress 0.0007587915
## Run 8 stress 0.000866098
## Run 9 stress 0.0004721406
## ... Procrustes: rmse 0.005032889 max resid 0.01223533
## Run 10 stress 0.0005079859
## Run 11 stress 0.0004634788
## ... Procrustes: rmse 0.005321765 max resid 0.0183867
## Run 12 stress 0.000465072
## ... Procrustes: rmse 0.005371227 max resid 0.01475996
## Run 13 stress 0.0007384817
## Run 14 stress 0.000394824
## ... Procrustes: rmse 0.004605859 max resid 0.01188218
## Run 15 stress 0.000518258
## Run 16 stress 0.0005136734
## Run 17 stress 0.000473039
## ... Procrustes: rmse 0.005138637 max resid 0.01622302
## Run 18 stress 0.0005788303
## Run 19 stress 0.0004015713
## ... Procrustes: rmse 0.005131142 max resid 0.01933418
## Run 20 stress 0.0007347459
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0003821989
## ... Procrustes: rmse 0.004476456 max resid 0.01095567
## Run 2 stress 0.0004461684
## ... Procrustes: rmse 0.004955654 max resid 0.01499453
## Run 3 stress 0.0003668378
## ... Procrustes: rmse 0.004393967 max resid 0.008933754
## ... Similar to previous best
## Run 4 stress 0.0006056404
## Run 5 stress 0.0004126129
## ... Procrustes: rmse 0.004513838 max resid 0.009770411
## ... Similar to previous best
## Run 6 stress 0.0004918153
## ... Procrustes: rmse 0.005465414 max resid 0.0160581
## Run 7 stress 0.0004549366
## ... Procrustes: rmse 0.004693527 max resid 0.01213237
## Run 8 stress 0.000529182
## Run 9 stress 0.0005141795
## Run 10 stress 0.0005082289
## Run 11 stress 0.0003903534
## ... Procrustes: rmse 0.00452944 max resid 0.0119541
## Run 12 stress 0.0005189809
## Run 13 stress 0.0004385049
## ... Procrustes: rmse 0.004698398 max resid 0.01237512
## Run 14 stress 0.0006229466
## Run 15 stress 0.0003581857
## ... Procrustes: rmse 0.004201118 max resid 0.01099654
## Run 16 stress 0.0005436673
## Run 17 stress 0.0004776069
## ... Procrustes: rmse 0.005053746 max resid 0.01297039
## Run 18 stress 0.0004772436
## ... Procrustes: rmse 0.005025857 max resid 0.01216691
## Run 19 stress 0.0003721602
## ... Procrustes: rmse 0.004270967 max resid 0.009809534
## ... Similar to previous best
## Run 20 stress 0.0005126607
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004019234
## ... Procrustes: rmse 0.004533444 max resid 0.01234633
## Run 2 stress 0.0005133353
## Run 3 stress 0.0005655076
## Run 4 stress 0.0005768717
## Run 5 stress 0.000478123
## ... Procrustes: rmse 0.004954507 max resid 0.01271203
## Run 6 stress 0.0008374938
## Run 7 stress 0.0005370092
## Run 8 stress 0.0006193657
## Run 9 stress 0.0006861016
## Run 10 stress 0.0005618969
## Run 11 stress 0.0006143793
## Run 12 stress 0.0004406319
## ... Procrustes: rmse 0.005194143 max resid 0.01424841
## Run 13 stress 0.0005161696
## Run 14 stress 0.0005661574
## Run 15 stress 0.00041776
## ... Procrustes: rmse 0.004988723 max resid 0.01321047
## Run 16 stress 0.0004606636
## ... Procrustes: rmse 0.004861812 max resid 0.01231159
## Run 17 stress 0.0004377342
## ... Procrustes: rmse 0.005055119 max resid 0.01654559
## Run 18 stress 0.0004524103
## ... Procrustes: rmse 0.005285869 max resid 0.01770919
## Run 19 stress 0.0003976137
## ... Procrustes: rmse 0.004718745 max resid 0.014156
## Run 20 stress 0.0004927219
## ... Procrustes: rmse 0.005525857 max resid 0.01672111
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004193772
## ... Procrustes: rmse 0.004686056 max resid 0.01276435
## Run 2 stress 0.0004221538
## ... Procrustes: rmse 0.004828868 max resid 0.01339936
## Run 3 stress 0.0004318669
## ... Procrustes: rmse 0.004855748 max resid 0.01373132
## Run 4 stress 0.0004504515
## ... Procrustes: rmse 0.004998023 max resid 0.01238517
## Run 5 stress 0.0005695926
## Run 6 stress 0.0004079489
## ... Procrustes: rmse 0.004671392 max resid 0.01494327
## Run 7 stress 0.0006315154
## Run 8 stress 0.0004025266
## ... Procrustes: rmse 0.004764022 max resid 0.01296106
## Run 9 stress 0.0004376535
## ... Procrustes: rmse 0.004996028 max resid 0.0138257
## Run 10 stress 0.0005060977
## Run 11 stress 0.0005937262
## Run 12 stress 0.0004900329
## ... Procrustes: rmse 0.005242864 max resid 0.01562874
## Run 13 stress 0.0005332133
## Run 14 stress 0.0005381253
## Run 15 stress 0.0005295212
## Run 16 stress 0.0004312233
## ... Procrustes: rmse 0.004691479 max resid 0.01056047
## Run 17 stress 0.0003927881
## ... Procrustes: rmse 0.00454853 max resid 0.009918742
## ... Similar to previous best
## Run 18 stress 0.0006719391
## Run 19 stress 0.0005363235
## Run 20 stress 0.00074983
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0005236368
## Run 2 stress 0.0009755487
## Run 3 stress 0.0004721384
## ... Procrustes: rmse 0.005674737 max resid 0.02545835
## Run 4 stress 0.0006257409
## Run 5 stress 0.0003957379
## ... Procrustes: rmse 0.004788155 max resid 0.0123255
## Run 6 stress 0.0006845759
## Run 7 stress 0.0006755215
## Run 8 stress 0.0005303393
## Run 9 stress 0.0003979002
## ... Procrustes: rmse 0.005083971 max resid 0.01845139
## Run 10 stress 0.000395574
## ... Procrustes: rmse 0.00459981 max resid 0.01194673
## Run 11 stress 0.0003540009
## ... Procrustes: rmse 0.004765595 max resid 0.01826128
## Run 12 stress 0.0003955707
## ... Procrustes: rmse 0.004608488 max resid 0.01080273
## Run 13 stress 0.0004512104
## ... Procrustes: rmse 0.005486612 max resid 0.02081706
## Run 14 stress 0.0005456189
## Run 15 stress 0.0004532211
## ... Procrustes: rmse 0.004930553 max resid 0.01187482
## Run 16 stress 0.0004728354
## ... Procrustes: rmse 0.005077693 max resid 0.01719745
## Run 17 stress 0.000420513
## ... Procrustes: rmse 0.004924917 max resid 0.01470531
## Run 18 stress 0.0004211687
## ... Procrustes: rmse 0.005344954 max resid 0.02120713
## Run 19 stress 0.0006219744
## Run 20 stress 0.0005985718
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0003849695
## ... Procrustes: rmse 0.004595968 max resid 0.013751
## Run 2 stress 0.0004080449
## ... Procrustes: rmse 0.004639177 max resid 0.009779006
## ... Similar to previous best
## Run 3 stress 0.0004975438
## ... Procrustes: rmse 0.005274462 max resid 0.01487247
## Run 4 stress 0.0005188719
## Run 5 stress 0.0004101888
## ... Procrustes: rmse 0.004899145 max resid 0.01232175
## Run 6 stress 0.0007265683
## Run 7 stress 0.0003697567
## ... Procrustes: rmse 0.004772944 max resid 0.01615411
## Run 8 stress 0.0004027828
## ... Procrustes: rmse 0.004739352 max resid 0.01303041
## Run 9 stress 0.0003969871
## ... Procrustes: rmse 0.004579626 max resid 0.01616612
## Run 10 stress 0.0004375693
## ... Procrustes: rmse 0.004723532 max resid 0.01014235
## Run 11 stress 0.0004366475
## ... Procrustes: rmse 0.004984618 max resid 0.01427805
## Run 12 stress 0.0004681725
## ... Procrustes: rmse 0.005178754 max resid 0.01680358
## Run 13 stress 0.0005118307
## Run 14 stress 0.0005812064
## Run 15 stress 0.0006515012
## Run 16 stress 0.0004383101
## ... Procrustes: rmse 0.005239162 max resid 0.01672319
## Run 17 stress 0.0004823391
## ... Procrustes: rmse 0.005091969 max resid 0.01552579
## Run 18 stress 0.0003847079
## ... Procrustes: rmse 0.004595912 max resid 0.01091414
## Run 19 stress 0.0004241075
## ... Procrustes: rmse 0.004843037 max resid 0.01155878
## Run 20 stress 0.0004509059
## ... Procrustes: rmse 0.004961292 max resid 0.01367751
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.000674973
## Run 2 stress 0.0007877988
## Run 3 stress 0.0005180845
## Run 4 stress 0.0005762981
## Run 5 stress 0.0004674005
## ... Procrustes: rmse 0.005145946 max resid 0.01385535
## Run 6 stress 0.001177719
## Run 7 stress 0.0004829814
## ... Procrustes: rmse 0.005583394 max resid 0.01620118
## Run 8 stress 0.000422639
## ... Procrustes: rmse 0.00473135 max resid 0.01301675
## Run 9 stress 0.0004921124
## ... Procrustes: rmse 0.005614911 max resid 0.02007218
## Run 10 stress 0.0004643677
## ... Procrustes: rmse 0.005054227 max resid 0.01115994
## Run 11 stress 0.0004943529
## ... Procrustes: rmse 0.005486646 max resid 0.01942662
## Run 12 stress 0.0005188606
## Run 13 stress 0.0004736155
## ... Procrustes: rmse 0.005398312 max resid 0.01608717
## Run 14 stress 0.0004765935
## ... Procrustes: rmse 0.005104658 max resid 0.01637495
## Run 15 stress 0.0006275954
## Run 16 stress 0.0003944783
## ... Procrustes: rmse 0.00486284 max resid 0.0154605
## Run 17 stress 0.0004099759
## ... Procrustes: rmse 0.004901942 max resid 0.01569258
## Run 18 stress 0.000461668
## ... Procrustes: rmse 0.005339949 max resid 0.02185588
## Run 19 stress 0.0004353079
## ... Procrustes: rmse 0.004951124 max resid 0.01550179
## Run 20 stress 0.0004247351
## ... Procrustes: rmse 0.004866573 max resid 0.01532616
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004211627
## ... Procrustes: rmse 0.005399464 max resid 0.01685116
## Run 2 stress 0.0006495876
## Run 3 stress 0.000444137
## ... Procrustes: rmse 0.005421098 max resid 0.01621439
## Run 4 stress 0.0004446032
## ... Procrustes: rmse 0.004748319 max resid 0.01665641
## Run 5 stress 0.0004420901
## ... Procrustes: rmse 0.004938855 max resid 0.01814248
## Run 6 stress 0.0005175497
## Run 7 stress 0.0007217013
## Run 8 stress 0.0006917951
## Run 9 stress 0.0005819831
## Run 10 stress 0.0005461722
## Run 11 stress 0.0004619445
## ... Procrustes: rmse 0.005074063 max resid 0.0179441
## Run 12 stress 0.0004497957
## ... Procrustes: rmse 0.005702384 max resid 0.02528707
## Run 13 stress 0.000501003
## Run 14 stress 0.0003243497
## ... Procrustes: rmse 0.004069295 max resid 0.01006512
## Run 15 stress 0.0004324889
## ... Procrustes: rmse 0.005192646 max resid 0.01639804
## Run 16 stress 0.0004780882
## ... Procrustes: rmse 0.00542541 max resid 0.01532617
## Run 17 stress 0.000499468
## ... Procrustes: rmse 0.005788939 max resid 0.02298442
## Run 18 stress 0.0005019001
## Run 19 stress 0.0005428689
## Run 20 stress 0.0003848443
## ... Procrustes: rmse 0.004631369 max resid 0.01183669
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.000528101
## Run 2 stress 0.0005477698
## Run 3 stress 0.000476103
## ... Procrustes: rmse 0.005213205 max resid 0.0144384
## Run 4 stress 0.000443488
## ... Procrustes: rmse 0.005089883 max resid 0.01617792
## Run 5 stress 0.0004167702
## ... Procrustes: rmse 0.004851587 max resid 0.0159724
## Run 6 stress 0.0005855826
## Run 7 stress 0.0005207991
## Run 8 stress 0.0006425186
## Run 9 stress 0.000432794
## ... Procrustes: rmse 0.005122171 max resid 0.01475833
## Run 10 stress 0.0005412621
## Run 11 stress 0.0005758087
## Run 12 stress 0.0005253865
## Run 13 stress 0.000551593
## Run 14 stress 0.0006039365
## Run 15 stress 0.0009676665
## Run 16 stress 0.0004057731
## ... Procrustes: rmse 0.004770353 max resid 0.01082988
## Run 17 stress 0.001054572
## Run 18 stress 0.000597139
## Run 19 stress 0.001421052
## Run 20 stress 0.0005040688
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0003993857
## ... Procrustes: rmse 0.004822579 max resid 0.01289955
## Run 2 stress 0.001142956
## Run 3 stress 0.0009003492
## Run 4 stress 0.000535482
## Run 5 stress 0.0005033666
## Run 6 stress 0.000451072
## ... Procrustes: rmse 0.005283965 max resid 0.01844184
## Run 7 stress 0.0004871623
## ... Procrustes: rmse 0.005226793 max resid 0.0161706
## Run 8 stress 0.0007140729
## Run 9 stress 0.000398286
## ... Procrustes: rmse 0.00476833 max resid 0.01435978
## Run 10 stress 0.0007189067
## Run 11 stress 0.0007795582
## Run 12 stress 0.0006254932
## Run 13 stress 0.0004717136
## ... Procrustes: rmse 0.005933248 max resid 0.02231356
## Run 14 stress 0.0009121538
## Run 15 stress 0.0004108764
## ... Procrustes: rmse 0.0051609 max resid 0.01708081
## Run 16 stress 0.0006425304
## Run 17 stress 0.000410325
## ... Procrustes: rmse 0.005252605 max resid 0.01688582
## Run 18 stress 0.0005237198
## Run 19 stress 0.00086598
## Run 20 stress 0.0007276005
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0005155999
## Run 2 stress 0.0004899788
## ... Procrustes: rmse 0.005317086 max resid 0.02524392
## Run 3 stress 0.0006053325
## Run 4 stress 0.0005216737
## Run 5 stress 0.0005106472
## Run 6 stress 0.0005746181
## Run 7 stress 0.0004764314
## ... Procrustes: rmse 0.005104271 max resid 0.01437562
## Run 8 stress 0.0005795286
## Run 9 stress 0.0004601214
## ... Procrustes: rmse 0.005346898 max resid 0.01650301
## Run 10 stress 0.0005583001
## Run 11 stress 0.0006328677
## Run 12 stress 0.0003634761
## ... Procrustes: rmse 0.004529208 max resid 0.01265819
## Run 13 stress 0.000672465
## Run 14 stress 0.0004430792
## ... Procrustes: rmse 0.005067674 max resid 0.01646525
## Run 15 stress 0.0007803134
## Run 16 stress 0.0004252387
## ... Procrustes: rmse 0.004777723 max resid 0.01255981
## Run 17 stress 0.0006724624
## Run 18 stress 0.000549138
## Run 19 stress 0.0004753694
## ... Procrustes: rmse 0.005501417 max resid 0.01427236
## Run 20 stress 0.0004056256
## ... Procrustes: rmse 0.004873396 max resid 0.01378126
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0005400356
## Run 2 stress 0.0008055853
## Run 3 stress 0.0004856681
## ... Procrustes: rmse 0.005115334 max resid 0.01182241
## Run 4 stress 0.0006126835
## Run 5 stress 0.0005335075
## Run 6 stress 0.0005482584
## Run 7 stress 0.0003966436
## ... Procrustes: rmse 0.004621982 max resid 0.01269059
## Run 8 stress 0.000539081
## Run 9 stress 0.000677219
## Run 10 stress 0.000359527
## ... Procrustes: rmse 0.004583128 max resid 0.01292521
## Run 11 stress 0.0004860514
## ... Procrustes: rmse 0.005336674 max resid 0.01658845
## Run 12 stress 0.000494901
## ... Procrustes: rmse 0.005699813 max resid 0.02235214
## Run 13 stress 0.0005589346
## Run 14 stress 0.0004932174
## ... Procrustes: rmse 0.00593829 max resid 0.02157871
## Run 15 stress 0.0004632155
## ... Procrustes: rmse 0.005279462 max resid 0.01724422
## Run 16 stress 0.0004649234
## ... Procrustes: rmse 0.005571462 max resid 0.02355818
## Run 17 stress 0.0006530129
## Run 18 stress 0.0005403669
## Run 19 stress 0.0004984566
## ... Procrustes: rmse 0.005591758 max resid 0.02129321
## Run 20 stress 0.0004563227
## ... Procrustes: rmse 0.005074622 max resid 0.01605494
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0005494286
## Run 2 stress 0.0005145648
## Run 3 stress 0.0006290057
## Run 4 stress 0.0005146115
## Run 5 stress 0.0004219942
## ... Procrustes: rmse 0.004729983 max resid 0.01128555
## Run 6 stress 0.0006670187
## Run 7 stress 0.0004061363
## ... Procrustes: rmse 0.00454931 max resid 0.0107608
## Run 8 stress 0.0004482543
## ... Procrustes: rmse 0.004804847 max resid 0.01374689
## Run 9 stress 0.0005722982
## Run 10 stress 0.0003596983
## ... Procrustes: rmse 0.004375209 max resid 0.01008431
## Run 11 stress 0.0004515239
## ... Procrustes: rmse 0.00478109 max resid 0.01365902
## Run 12 stress 0.0005096998
## Run 13 stress 0.0005311039
## Run 14 stress 0.0005115606
## Run 15 stress 0.0003897566
## ... Procrustes: rmse 0.004648519 max resid 0.01070933
## Run 16 stress 0.0006634143
## Run 17 stress 0.0006131393
## Run 18 stress 0.0006460661
## Run 19 stress 0.0004272343
## ... Procrustes: rmse 0.004836545 max resid 0.01030769
## Run 20 stress 0.0004245322
## ... Procrustes: rmse 0.004694856 max resid 0.01055333
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0004455235
## ... Procrustes: rmse 0.005035378 max resid 0.01370612
## Run 2 stress 0.0004840853
## ... Procrustes: rmse 0.005431556 max resid 0.02354275
## Run 3 stress 0.0003901781
## ... Procrustes: rmse 0.004660615 max resid 0.01301871
## Run 4 stress 0.0006856975
## Run 5 stress 0.0004139996
## ... Procrustes: rmse 0.004649353 max resid 0.01454429
## Run 6 stress 0.0004613196
## ... Procrustes: rmse 0.005159429 max resid 0.02318408
## Run 7 stress 0.0004865776
## ... Procrustes: rmse 0.005194842 max resid 0.01268464
## Run 8 stress 0.0005549931
## Run 9 stress 0.0005067894
## Run 10 stress 0.0004430163
## ... Procrustes: rmse 0.004752064 max resid 0.01338333
## Run 11 stress 0.0004723749
## ... Procrustes: rmse 0.005075101 max resid 0.01525391
## Run 12 stress 0.000399265
## ... Procrustes: rmse 0.004517802 max resid 0.01050185
## Run 13 stress 0.0006961381
## Run 14 stress 0.0004865672
## ... Procrustes: rmse 0.005177302 max resid 0.01198743
## Run 15 stress 0.000436846
## ... Procrustes: rmse 0.004621057 max resid 0.01105262
## Run 16 stress 0.0004985944
## ... Procrustes: rmse 0.005374871 max resid 0.01407973
## Run 17 stress 0.0003887923
## ... Procrustes: rmse 0.004608321 max resid 0.00941683
## ... Similar to previous best
## Run 18 stress 0.0005091787
## Run 19 stress 0.0005212327
## Run 20 stress 0.0006659852
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0005184044
## Run 2 stress 0.0005011294
## Run 3 stress 0.0004661713
## ... Procrustes: rmse 0.0054855 max resid 0.02214306
## Run 4 stress 0.0004749515
## ... Procrustes: rmse 0.005281145 max resid 0.01668199
## Run 5 stress 0.0003733597
## ... Procrustes: rmse 0.00472797 max resid 0.01607216
## Run 6 stress 0.0004053856
## ... Procrustes: rmse 0.004710506 max resid 0.01696176
## Run 7 stress 0.0005636963
## Run 8 stress 0.0006892321
## Run 9 stress 0.000550203
## Run 10 stress 0.0003921546
## ... Procrustes: rmse 0.004890505 max resid 0.01735947
## Run 11 stress 0.0004650498
## ... Procrustes: rmse 0.004811018 max resid 0.01952996
## Run 12 stress 0.0005330389
## Run 13 stress 0.0004803663
## ... Procrustes: rmse 0.005667154 max resid 0.01670069
## Run 14 stress 0.0007789463
## Run 15 stress 0.001733128
## Run 16 stress 0.0004180843
## ... Procrustes: rmse 0.005243979 max resid 0.02302835
## Run 17 stress 0.00077982
## Run 18 stress 0.0005308876
## Run 19 stress 0.0005371117
## Run 20 stress 0.0004370248
## ... Procrustes: rmse 0.005243395 max resid 0.01732859
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit# Note: results are hidden (too long)6
Discuss the stress (or SStress) of each dimensional solution. Make a scree plot if you’re able.
#plot stress results
plot(c(1:5), results[21, ], type = "b", col = "blue", lwd = 3,
ylim = c(0, max(results)), xlab = "Dimensions", ylab = "Stress", pch = 19,
main = "MDS for Rural-Urban Data, Euclidean Distance")
mins <- apply(results[1:20, ], 2, min)
maxs <- apply(results[1:20, ], 2, max)
meds <- apply(results[1:20, ], 2, median)
for (i in 1:5){
points(rep(i, 3), c(mins[i], meds[i], maxs[i]), type = "b", col = "red", lwd = 3, pch = 19)
}
legend(3.5, (.9*max(results)), c("MDS Solution", "20 Permutations"), lwd = 3, col = c("blue", "red"))
After performing multidimensional scaling for 1-5 dimensions, the above scree plot for stress illustrates an elbow at 2 dimensions. This stress level is below 10% and indicates a good fit. For 3 dimensions, the stress is below 5% and indicates an excellent fit. After 3 dimensions, random chance could result in comparable stress values.
Stress is a measure of the difference between actual pairwise distances and calculated reference distances; a lower stress indicates a better fit. As the dimensions exceeds that of the data (for 4 and 5 dimensions), the stress goes to 0.
7
Make a two dimensional plot of your MDS results.
data_ord_base.mds2 <- metaMDS(data_ord_base, k = 2, distance = "euclidean")## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0762502
## Run 1 stress 0.0762502
## ... Procrustes: rmse 6.666662e-06 max resid 4.201412e-05
## ... Similar to previous best
## Run 2 stress 0.08193692
## Run 3 stress 0.1104296
## Run 4 stress 0.07130037
## ... New best solution
## ... Procrustes: rmse 0.03267168 max resid 0.2604157
## Run 5 stress 0.1222007
## Run 6 stress 0.1064976
## Run 7 stress 0.0819463
## Run 8 stress 0.0762502
## Run 9 stress 0.0713005
## ... Procrustes: rmse 6.228924e-05 max resid 0.0003496877
## ... Similar to previous best
## Run 10 stress 0.08193569
## Run 11 stress 0.1140951
## Run 12 stress 0.08193569
## Run 13 stress 0.08194625
## Run 14 stress 0.07625021
## Run 15 stress 0.0713004
## ... Procrustes: rmse 2.885257e-05 max resid 0.0001491525
## ... Similar to previous best
## Run 16 stress 0.08194625
## Run 17 stress 0.08614369
## Run 18 stress 0.08194626
## Run 19 stress 0.07130101
## ... Procrustes: rmse 0.0001769265 max resid 0.000993719
## ... Similar to previous best
## Run 20 stress 0.07130039
## ... Procrustes: rmse 3.533542e-05 max resid 0.0001839468
## ... Similar to previous best
## *** Solution reachedplot(data_ord_base.mds2, type = "t")
stressplot(data_ord_base.mds2)
The R-squared values seem sufficiently high with the two dimensional MDS result.
8
If possible, overlay some other continuous variable(s) to interpret your ordination axes. Calculate p-values for the overlaid additional variable(s). If you can, get some non-linear wireplots of the these overlaid variables (see examples online in R).
We can also add environmental variables to our plot.
fig <- ordiplot(data_ord_base.mds2, type = "none", cex = 1.1)
text(fig, "species", col = "red", cex = 1.1)
text(fig, "sites", col = "blue", cex = 0.8)
fit <- envfit(data_ord_base.mds2, data_ord_env, permutations = 1000)
plot(fit, col = "black", lwd = 3)
fit <- envfit(data_ord_base_ca, data_ord_env, permutations = 1000)
fit##
## ***VECTORS
##
## CA1 CA2 r2 Pr(>r)
## Unemployment_Rate_2019 0.93609 -0.35176 0.2400 0.000999 ***
## Civilian_Labor_Force_2019_as_pct -0.97424 -0.22551 0.4110 0.000999 ***
## Percent_Adults_Bachelors_or_Higher -0.99468 -0.10305 0.6962 0.000999 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 1000The three overlaid continuous variables above are all significant with p<0.05. This is graphically suggested by the long length of the lines.
mds4 <- metaMDS(data_ord_env, distance="euclidean", k=4)## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0
## Run 1 stress 0.0007227778
## Run 2 stress 0.0007894462
## Run 3 stress 0.0009252429
## Run 4 stress 0.000754978
## Run 5 stress 0.0007677275
## Run 6 stress 0.0006250545
## Run 7 stress 0.000780112
## Run 8 stress 0.0005232291
## Run 9 stress 0.004746901
## Run 10 stress 0.0008708487
## Run 11 stress 0.0007830212
## Run 12 stress 0.0008947836
## Run 13 stress 0.0009902119
## Run 14 stress 0.001028639
## Run 15 stress 0.0008125473
## Run 16 stress 0.0005889211
## Run 17 stress 0.0006813661
## Run 18 stress 0.0007503506
## Run 19 stress 0.0005297504
## Run 20 stress 0.0006387298
## *** No convergence -- monoMDS stopping criteria:
## 20: no. of iterations >= maxit## Warning in metaMDS(data_ord_env, distance = "euclidean", k = 4): stress is
## (nearly) zero: you may have insufficient datafig <- ordiplot(mds4, type = "none", cex = 1.1, main = "NMDS for COVID-19 Data")
text(fig, "species", col = "red", cex = 0.7)
text(fig, "sites", col = "black", cex = 0.7)
plot(fit)
tmp1 <- with(data_ord_env, ordisurf(mds4, Unemployment_Rate_2019, add = TRUE))
tmp2 <- with(data_ord_env, ordisurf(mds4, Percent_Adults_Bachelors_or_Higher, add = TRUE, col = "green4"))
tmp3 <- with(data_ord_env, ordisurf(mds4, Civilian_Labor_Force_2019_as_pct, add = TRUE, col = "purple"))
vis.gam(tmp1, main = "Unemployment Rate")
vis.gam(tmp2, main = "Percentage of Adults with Bachelor's or Higher")
vis.gam(tmp3, main = "Civilian Labor Force Percentage")
9
Again, assuming you have at least one additional continuous variable, perform canonical correspondence analysis.
As directed, here we’ll perform CCA – both with and without (or the other way around) the environmental variables.
data_ord_base_cca1 <- cca(data_ord_base, scale="FALSE")
data_ord_base_cca2 <- cca(data_ord_base, data_ord_env, scale="FALSE")
plot(data_ord_base_cca1, main="CCA without env")
plot(data_ord_base_cca2, main="CCA with env")
#plot(data_ord_base_cca, main = "CCA for Rural-Urban Type", type = "n")
#points(data_ord_base_cca, pch = 19, col = "red", cex = 1)
#text(data_ord_base_cca, "species", col = "blue", cex = 0.7)
#text(data_ord_base_cca, display = c("sites"), labels = rownames(data_ord_base), cex = 0.5)
(fit_cca <- envfit(data_ord_base_cca2, data_ord_env, permutations=1000))##
## ***VECTORS
##
## CCA1 CCA2 r2 Pr(>r)
## Unemployment_Rate_2019 0.977760 -0.209739 0.2553 0.000999 ***
## Civilian_Labor_Force_2019_as_pct -0.997160 -0.075256 0.4131 0.000999 ***
## Percent_Adults_Bachelors_or_Higher -0.999830 -0.018480 0.7048 0.000999 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 1000plot(data_ord_base_cca2)
plot(fit_cca, col = "red", lwd = 3)
summary(data_ord_base_cca2)##
## Call:
## cca(X = data_ord_base, Y = data_ord_env, scale = "FALSE")
##
## Partitioning of scaled Chi-square:
## Inertia Proportion
## Total 0.05033 1.0000
## Constrained 0.02673 0.5312
## Unconstrained 0.02360 0.4688
##
## Eigenvalues, and their contribution to the scaled Chi-square
##
## Importance of components:
## CCA1 CCA2 CCA3 CA1 CA2 CA3
## Eigenvalue 0.02517 0.001433 0.0001286 0.01225 0.00795 0.002016
## Proportion Explained 0.50014 0.028465 0.0025542 0.24348 0.15796 0.040061
## Cumulative Proportion 0.50014 0.528601 0.5311551 0.77463 0.93259 0.972652
## CA4
## Eigenvalue 0.001376
## Proportion Explained 0.027348
## Cumulative Proportion 1.000000
##
## Accumulated constrained eigenvalues
## Importance of components:
## CCA1 CCA2 CCA3
## Eigenvalue 0.02517 0.001433 0.0001286
## Proportion Explained 0.94160 0.053590 0.0048088
## Cumulative Proportion 0.94160 0.995191 1.0000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
##
##
## Species scores
##
## CCA1 CCA2 CCA3
## Always_Wear_Mask_Survey -0.05278 -0.05184 0.004032
## Median_Household_Income_Percent_of_State_Total_2019 -0.09263 0.02673 -0.003443
## Percent_Poverty_2019 0.28361 0.01487 -0.020196
## Percent_Adults_Less_Than_HS 0.39865 -0.01652 0.001006
## Covid_Confirmed_Cases_as_pct 0.17152 0.06858 0.043256
## CA1 CA2 CA3
## Always_Wear_Mask_Survey -0.03731 0.12488 -0.002997
## Median_Household_Income_Percent_of_State_Total_2019 0.09936 -0.03903 0.005827
## Percent_Poverty_2019 -0.22620 -0.08500 0.111714
## Percent_Adults_Less_Than_HS -0.16894 -0.05727 -0.102570
## Covid_Confirmed_Cases_as_pct -0.12422 -0.18453 -0.063076
##
##
## Site scores (weighted averages of species scores)
##
## CCA1 CCA2 CCA3 CA1 CA2 CA3
## Alachua -0.44270 -3.40786 -0.24161 -2.85980 0.330773 1.25210
## Baker 0.10024 4.26789 0.42300 1.55293 -0.777995 0.29274
## Bay -0.64438 1.89645 3.41489 1.04832 -1.052120 0.56516
## Bradford 1.58692 3.23318 -4.78274 -0.08183 -1.114071 0.46772
## Brevard -1.20371 -0.70458 -2.04920 0.64061 0.584208 0.35922
## Broward -0.78323 -2.24673 4.48190 -0.56799 0.490985 -0.42667
## Calhoun 1.65422 -0.23416 2.50777 -0.54201 -0.193127 -0.38618
## Charlotte -0.85407 -1.79553 -2.14568 0.79143 1.385045 0.58618
## Citrus -0.20269 -1.81547 -3.34039 0.73548 0.866036 1.24778
## Clay -1.44785 4.10021 -2.85479 2.36989 -0.826960 0.41909
## Collier -1.06933 1.44385 -1.13605 0.10109 -0.693334 -1.60439
## Columbia 0.53112 3.77349 1.32211 0.49487 -1.132029 0.77115
## DeSoto 1.65614 -4.61067 1.16665 -1.24409 1.679176 -1.08893
## Dixie 1.92664 1.34252 -6.60205 -0.62286 -0.748921 1.16633
## Duval -0.59565 0.02211 1.40287 -0.13757 -0.465944 0.39331
## Escambia -0.27687 1.74232 1.67822 -0.22159 -0.703872 1.20944
## Flagler -1.31372 0.20796 -4.24471 1.62497 0.553084 0.85203
## Franklin 1.27565 2.79012 -1.24754 -0.56045 -1.369445 -0.23333
## Gadsden 1.32128 -1.15008 4.38857 -1.08992 -0.501499 -0.58992
## Gilchrist 0.37703 1.16008 -4.16196 0.72436 0.130178 0.93945
## Glades 1.14550 -4.10171 -3.33032 -0.12684 1.473841 -0.30031
## Gulf 0.32654 3.40464 7.44655 0.81659 -2.320638 -0.66988
## Hamilton 2.92405 2.86542 -11.62673 -1.93242 -1.893437 3.02394
## Hardee 1.96030 -0.03744 -1.83912 -0.69453 -1.048443 -0.31393
## Hendry 2.01789 -3.18102 2.53173 -0.30451 -0.804561 -2.95680
## Hernando -0.36066 -1.67076 -2.82344 1.06470 0.998128 0.50630
## Highlands 0.26128 -3.16753 -1.63842 0.06873 1.183650 0.38727
## Hillsborough -0.71013 -1.63661 -0.72228 -0.59068 0.236228 0.02218
## Holmes 1.70129 -1.95197 3.75463 -0.98807 0.815789 -0.73717
## Indian River -0.80417 0.13399 -2.23177 0.48561 -0.003610 -0.15747
## Jackson 1.43155 -0.29918 6.38724 -0.94451 -0.007011 -0.43450
## Jefferson 0.56973 -2.86330 2.89773 -1.17235 1.130851 -0.60445
## Lafayette 1.94225 4.61041 15.16637 -1.27467 -1.769550 -3.32407
## Lake -0.82846 -0.95936 -0.81247 0.92437 1.089037 0.26855
## Lee -0.79304 -0.31602 -0.35654 0.36711 0.453950 -0.39778
## Leon -0.44762 -1.03335 -1.77355 -2.97313 -1.020685 1.87070
## Levy 0.68588 -3.08008 -3.45481 -0.10012 1.332323 1.50243
## Liberty 1.47275 1.42754 0.60829 -0.79446 -0.277589 0.99307
## Madison 2.15379 3.10521 -4.23025 -1.34032 -2.244500 1.29918
## Manatee -0.90616 0.51169 -0.76392 0.39430 0.158330 -0.19494
## Marion -0.01206 -0.42917 -2.30415 0.33564 0.456923 0.80712
## Martin -1.38051 -0.43010 -0.93709 0.49063 0.525289 -0.53174
## Miami-Dade 0.30614 -1.71364 10.82034 -1.67193 0.359637 -1.97126
## Monroe -1.31414 -2.14927 2.34747 -0.07716 0.763749 0.07965
## Nassau -1.31454 5.01949 -2.01014 1.71006 -1.252636 0.07229
## Okaloosa -1.03147 3.96982 -1.07972 0.72880 -0.963809 0.20686
## Okeechobee 1.13767 -4.39348 0.98386 -0.43563 1.593806 -1.01245
## Orange -0.79477 -1.25250 0.55677 -0.56422 -0.031170 -0.22220
## Osceola -0.26909 -2.68968 5.13622 0.14793 1.049223 0.03052
## Palm Beach -0.95756 -1.79612 1.17823 -0.58413 0.254155 -0.87391
## Pasco -0.80740 -2.85309 -0.58236 0.59090 1.567402 0.24828
## Pinellas -0.99830 -3.07182 1.02956 -0.29765 1.202111 0.27183
## Polk -0.03103 -1.74815 0.06866 0.23412 0.697029 -0.14035
## Putnam 1.25636 -2.27366 -5.04933 -0.62878 0.492432 1.52447
## St. Johns -2.07921 5.17633 -3.83043 0.81310 -1.728165 -0.66101
## St. Lucie -0.57847 -1.51729 -0.02183 1.10796 0.643239 -0.43374
## Santa Rosa -1.10287 4.72538 -0.52166 1.32545 -1.239094 0.10723
## Sarasota -1.56170 -0.88287 0.12730 0.35835 0.902196 -0.52889
## Seminole -1.68298 -0.48667 -2.54127 0.12969 0.054256 0.43293
## Sumter -1.31980 -0.04108 -1.78500 0.78670 0.750345 -0.72767
## Suwannee 1.05876 4.31106 0.78212 0.23530 -1.765324 -0.34052
## Taylor 1.69637 0.84303 3.43101 -0.16838 -0.384565 -0.46401
## Union 1.33550 1.95629 -0.08314 0.26188 0.379401 -0.54734
## Volusia -0.64360 -1.35740 -2.70563 0.47984 0.739835 1.14598
## Wakulla -0.37721 4.08455 -0.28765 1.52163 -0.774887 0.30464
## Walton -0.69538 2.82575 1.12300 0.48687 -0.468831 -0.75593
## Washington 1.19601 -1.18162 0.88880 -0.50963 0.689445 0.59098
##
##
## Site constraints (linear combinations of constraining variables)
##
## CCA1 CCA2 CCA3 CA1 CA2 CA3
## Alachua -2.007956 -0.002997 -0.399842 -2.85980 0.330773 1.25210
## Baker 0.922848 0.890041 0.902784 1.55293 -0.777995 0.29274
## Bay -0.084847 -1.772954 0.592189 1.04832 -1.052120 0.56516
## Bradford 1.207997 1.058849 0.995538 -0.08183 -1.114071 0.46772
## Brevard -0.688836 -0.098129 0.142918 0.64061 0.584208 0.35922
## Broward -0.995305 -0.641658 0.970594 -0.56799 0.490985 -0.42667
## Calhoun 1.299548 -0.122155 -0.382269 -0.54201 -0.193127 -0.38618
## Charlotte -0.020235 0.283009 -0.982653 0.79143 1.385045 0.58618
## Citrus 0.557753 -0.969861 -2.092434 0.73548 0.866036 1.24778
## Clay -0.197145 -0.107359 1.164709 2.36989 -0.826960 0.41909
## Collier -1.354230 0.267885 -0.607522 0.10109 -0.693334 -1.60439
## Columbia 0.696933 0.569731 0.755388 0.49487 -1.132029 0.77115
## DeSoto 1.138442 0.585270 0.344483 -1.24409 1.679176 -1.08893
## Dixie 1.351199 0.389223 -0.060075 -0.62286 -0.748921 1.16633
## Duval -0.721987 -0.975451 0.769796 -0.13757 -0.465944 0.39331
## Escambia -0.393925 0.069627 0.246089 -0.22159 -0.703872 1.20944
## Flagler -0.166712 -0.352844 -0.719791 1.62497 0.553084 0.85203
## Franklin 0.574643 0.521513 -0.125193 -0.56045 -1.369445 -0.23333
## Gadsden 0.570257 -1.149294 0.011786 -1.08992 -0.501499 -0.58992
## Gilchrist 0.858024 0.652154 0.278065 0.72436 0.130178 0.93945
## Glades 1.258029 -0.506087 0.528679 -0.12684 1.473841 -0.30031
## Gulf 0.444904 -2.698311 -0.367362 0.81659 -2.320638 -0.66988
## Hamilton 1.397363 0.529928 -0.980435 -1.93242 -1.893437 3.02394
## Hardee 1.253258 -1.481501 -1.430620 -0.69453 -1.048443 -0.31393
## Hendry 1.393228 -4.009958 -0.790186 -0.30451 -0.804561 -2.95680
## Hernando 0.530182 -0.659333 -0.817613 1.06470 0.998128 0.50630
## Highlands 0.601215 -0.760695 -1.457619 0.06873 1.183650 0.38727
## Hillsborough -1.053212 -0.450856 0.441390 -0.59068 0.236228 0.02218
## Holmes 1.263857 0.876267 0.155464 -0.98807 0.815789 -0.73717
## Indian River -0.546316 -0.293234 -1.144739 0.48561 -0.003610 -0.15747
## Jackson 0.945306 0.485231 -0.005222 -0.94451 -0.007011 -0.43450
## Jefferson 0.092725 0.825488 -0.363288 -1.17235 1.130851 -0.60445
## Lafayette 0.756734 2.215306 -0.388922 -1.27467 -1.769550 -3.32407
## Lake -0.009966 0.412752 0.248184 0.92437 1.089037 0.26855
## Lee -0.520889 0.403451 0.042881 0.36711 0.453950 -0.39778
## Leon -2.335794 -0.541335 -0.684923 -2.97313 -1.020685 1.87070
## Levy 0.988017 -0.273134 0.567823 -0.10012 1.332323 1.50243
## Liberty 1.065071 1.340765 -0.798182 -0.79446 -0.277589 0.99307
## Madison 0.867993 -0.465183 0.385345 -1.34032 -2.244500 1.29918
## Manatee -0.661535 0.516213 -0.210707 0.39430 0.158330 -0.19494
## Marion 0.350330 0.080264 -0.686281 0.33564 0.456923 0.80712
## Martin -1.034645 0.355132 -0.395475 0.49063 0.525289 -0.53174
## Miami-Dade -0.656128 0.877023 1.313950 -1.67193 0.359637 -1.97126
## Monroe -1.202339 -0.400639 2.963260 -0.07716 0.763749 0.07965
## Nassau -0.567587 0.591939 0.341978 1.71006 -1.252636 0.07229
## Okaloosa -0.790901 1.113859 0.119242 0.72880 -0.963809 0.20686
## Okeechobee 1.091179 -0.207662 1.140160 -0.43563 1.593806 -1.01245
## Orange -1.191455 -0.644449 1.058354 -0.56422 -0.031170 -0.22220
## Osceola 0.145779 -0.756823 1.364936 0.14793 1.049223 0.03052
## Palm Beach -1.330926 -0.477918 -0.338012 -0.58413 0.254155 -0.87391
## Pasco -0.082094 -0.112526 -0.078787 0.59090 1.567402 0.24828
## Pinellas -0.882716 -0.236182 0.647977 -0.29765 1.202111 0.27183
## Polk 0.250653 -0.446754 0.049231 0.23412 0.697029 -0.14035
## Putnam 1.037210 -0.715389 -0.546727 -0.62878 0.492432 1.52447
## St. Johns -2.100531 0.890748 -0.620499 0.81310 -1.728165 -0.66101
## St. Lucie 0.196923 -1.166346 0.217540 1.10796 0.643239 -0.43374
## Santa Rosa -0.545711 0.637809 0.042468 1.32545 -1.239094 0.10723
## Sarasota -1.176335 0.780044 -0.981018 0.35835 0.902196 -0.52889
## Seminole -1.613426 -0.471502 0.472865 0.12969 0.054256 0.43293
## Sumter -0.681182 0.808735 -4.615416 0.78670 0.750345 -0.72767
## Suwannee 0.788376 0.307791 0.576808 0.23530 -1.765324 -0.34052
## Taylor 1.516638 0.180899 0.861904 -0.16838 -0.384565 -0.46401
## Union 1.519029 2.642363 -0.115282 0.26188 0.379401 -0.54734
## Volusia -0.128104 -0.398469 0.452265 0.47984 0.739835 1.14598
## Wakulla 0.406747 0.785360 1.065397 1.52163 -0.774887 0.30464
## Walton -0.547063 1.422236 -0.247075 0.48687 -0.468831 -0.75593
## Washington 1.105397 0.681665 0.482510 -0.50963 0.689445 0.59098
##
##
## Biplot scores for constraining variables
##
## CCA1 CCA2 CCA3 CA1 CA2 CA3
## Unemployment_Rate_2019 0.5473 -0.60888 -0.57427 0 0 0
## Civilian_Labor_Force_2019_as_pct -0.7554 -0.18958 0.62725 0 0 0
## Percent_Adults_Bachelors_or_Higher -0.9991 0.02401 -0.03542 0 0 0The three overlaid continuous variables above are all significant with p<0.001. However, the continuous variables don’t have a great distribution on this plot, so the discriminating ability is probably not as helpful as what we might like.
10
Finally, write a paragraph or so comparing the methods you’ve used, discuss what conclusions you reach, etc.
The counties are well distributed across the quadrants in each of our MDS methods, and we find significance in three of our environmental variables. Our two-dimensional MDS results are robust and suggest two dimensions are likely optimal, although three dimensions could also be considered. Our results for canonical correspondence analysis (CCA) are somewhat concentrated and difficult to read. In CCA, we find substantially more variation on the second CCA axis, which is inversely related to unemployment. Although our relatively high amount of counties (67) contributes to the difficulty in discerning the plot, the CCA plot is particularly concentrated. We believe the NMDS plot in #8 with contour lines optimally illustrates the distribution of the counties and their relations to the NMDS axes and environmental variables. It conveys a lot of information in a single plot. Moreover, we can see that the contour lines are not exactly perpendicular to their respective blue dimensional axes, suggesting a more complex (non-linear) significant pattern of counties according to the environmental variables of unemployment, bachelor’s percentage, and civilian labor force percentage.